mid-chapter quiz solve each inequality. then graph it on a … · 2014. 8. 27. · mid-chapter...
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Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 1
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 2
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 3
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 4
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 5
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 6
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 7
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 8
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 9
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 10
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 11
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 12
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
62/87,21���
The solution set is {p | p < í3}.
��������t í 9
62/87,21���
The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.eSolutions Manual - Powered by Cognero Page 13
Mid-Chapter Quiz
Solve each inequality. Then graph it on a number line.���x í 8 > 4
62/87,21���
The solution set is {x | x > 12}.
���m �������
62/87,21���
The solution set is {m | m � 4}.
���p í 4 < í7
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The solution set is {p | p < í3}.
��������t í 9
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The solution set is {t | t � 21}.
���&21&(576� Lupe¶s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. D�� Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. E�� She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket.
62/87,21���a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $15 after buying a concert ticket. � b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write aninequality. Because she can spend at most $60, the inequality symbol is �� �
� Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket.
Define a variable, write an inequality, and solve each problem. Check your solution.���The sum of a number and í2 is no more than 6.
62/87,21���Sample answer: Let x = the number. The word ³sum´�means addition, and the phrase ³no more than´�means the same as less than or equal to. �
� The solution set is {x | x � 8}. � Check the endpoint with 8 and the direction with a value less than 8. �
�
�
���A number decreased by 4 is more than í1.
62/87,21���Sample answer: Let x = the number. The phrase ³decreased by´�means subtraction, and the phrase ³more than´�means greater than. �
� The solution set is {x | x > 3}. � Check the endpoint with 3 and the direction with a value greater than 3. �
�
�
���Twice a number increased by 3 is less than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. The word ³twice´�means to multiply by 2, and the phrase ³decreased by´�means to subtract. �
� The solution set is {x | x < í7}. � Check the endpoint with -7 and the direction with a value less than -7. �
�
��������� �
���08/7,3/(�&+2,&(� Jane is saving money to buy a new cell phone that costs no more than $90. So far, she hassaved $52. How much more money does Jane need to save? $��$38 %��more than $38 &��no more than $38 '��at least $38
62/87,21���Let c be the amount Jane still needs to save. Write an inequality. The phrase ³no more than´�means the same as lessthan or equal to. �
� So, Jane needs to save no more than $38. The correct choice is choice C.
Solve each inequality. Check your solution.����
62/87,21���
� The solution set is {y | y � 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then
or 6 � 5, so the solution checks.
����4 <
62/87,21���
The solution set is {c | c > 20}.
To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then �RU���!����VR�
the solution checks.
����í8x > 24
62/87,21���
The solution set is {x | x < í3}. To check this answer, substitute a number less than í3 into the original inequality. If x = í4, then í8(í4) or 32 > 24, so the solution checks.
����2m�� í10
62/87,21���
The solution set is {m | m � í5}. To check this answer, substitute a number less than or equal to í5 into the original inequality. If m = í6, then 2(í6) or í12 � í10, so the solution checks.
���� <
62/87,21���
The solution set is .
To check this answer, substitute a number less than �LQWR�WKH�RULJLQDO�LQHTXDOLW\��,I�x = 1, then , so the
solution checks.
����í9a�� í45
62/87,21���
The solution set is {a | a � 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then í9(2) or í18 � í45, so the solution checks.
���� > í3
62/87,21���
The solution set is {w | w > í18}.
To check this answer, substitute a number greater than í18 into the original inequality. If w = í12, then �RU í2 >
í3, so the solution checks.
���� < í2
62/87,21���
The solution set is {k | k < í14}.
To check this answer, substitute a number less than í14 into the original inequality. If k = í21, then �RU í3 < í2,
so the solution checks.
����$1,0$/6� The world¶s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weighup to 40 pounds. D�� Write inequalities to describe the ranges of lengths and weights of male bustards. E�� Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards.
62/87,21���a. Let �EH�WKH�OHQJWK�RI�D�PDOH�EXVWDUG��DQG�OHW�w be the weight of a male bustard. The phrase ³up to´�means the same as less than. Both the length and weight of a bustard must be more than zero. � 0 < �< 4 0 < w < 40 � b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. �
����*$5'(1,1*� Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find themaximum length of a side of the garden.
62/87,21���Let x be the side length of Bill¶s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. �
� So, the garden can be at most 15 feet on each side.
Solve each inequality. Check your solution.����4a í 2 > 14
62/87,21���
� The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5.�
� So, the solution checks.
����2x���������x í 10
62/87,21���
� The solution set is {x | x � 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10.�
� So, the solution checks.
����íp + 4 < í9
62/87,21���
� The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15.�
� So, the solution checks.
���� ����� í3
62/87,21���
� The solution set is {d | d � í16}. To check this answer, substitute a number greater than or equal to í16 into the original inequality. Let d = í12.�
� So, the solution checks.
����í2(4b + 1) < í3b + 8
62/87,21���
� The solution set is {b | b > í2}. To check this answer, substitute a number greater than í2 into the original inequality. Let b = 0.�
� So, the solution checks.
Define a variable, write an inequality, and solve each problem. Check your solution.����Three times a number increased by 8 is no more than the number decreased by 4.
62/87,21���Sample answer: Let x = the number. ³Times´�means multiplication, ³increased by´�means addition, ³no more than´�means less than or equal to, and ³decreased by´�means subtraction. �
� The solution set is {x | x � í6}. To check this answer, substitute a number less than or equal to í6 into the original inequality. Let x = í7. �
� So, the solution checks.
����Two thirds of a number plus 5 is greater than 17.
62/87,21���Sample answer: Let x = the number. ³Of´�means multiplication. �
� The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21.�
� So, the solution checks.
����08/7,3/(�&+2,&(� Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? )� 2 *� 3 +� 4 -� 5
62/87,21���Let g be the number of games Kyle bowls. �
� The solution set is .
Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H.
eSolutions Manual - Powered by Cognero Page 14
Mid-Chapter Quiz