Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Unit 2 Study Guide

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Solve 44 = 14 − 2a.

a. a = 15 c. a = –29

b. a = 29 d. a = –15

____ 2. Solve f

45−

2

9=

2

9.

a. f = 20 c. f = −20

b. f = −101 d. f = 101

____ 3. Solve 43a + 10 − 26a = 27.

a. a = 1 c. a = −17b. a = 17 d. a = −1

____ 4. Devon pays $24.95 for her roller skates. After that she pays $3.95 for each visit to the roller rink. What is the

greatest number of visits she can afford if the total amount she spends cannot be more than $76.30?

a. 3 c. 51

b. 13 d. 19

____ 5. If 8y – 8 = 24, find the value of 2y.

a. 2 c. 11

b. 8 d. 24

____ 6. The formula p = nc − e gives the profit p when a number of items n are each sold at a cost c and expenses e

are subtracted. If p = 3750, n = 3000, and e = 900, what is the value of c?

a. 0.80 c. 1.55

b. 1.25 d. 0.95

____ 7. Solve 50q − 43 = 52q − 81.

a. q = 38 c. q = −38

b. q = −19 d. q = 19

____ 8. Solve n − 8 + n = 1 − 4n.

a. n = −41

2c. n = −1

1

6

b. n = 11

2d. n = 3

1

2

____ 9. Solve −6m − 6 + 8m = −5 + 2m − 1. Tell whether the equation has infinitely many solutions or no solutions.

a. Two solutions c. Only one solution

b. Infinitely many solutions d. No solutions

Name: ________________________ ID: A

2

____ 10. A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per

movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?a. 9 movies c. 3 movies

b. 5 movies d. 7 movies

____ 11. Find three consecutive integers such that twice the greatest integer is 2 less than 3 times the least integer.

a. 8, 9, 10 c. 2, 3, 4

b. 4, 5, 6 d. 6, 7, 8

____ 12. A professional cyclist is training for the Tour de France. What was his average speed in miles per hour if he

rode the 120 miles from Laval to Blois in 4.7 hours? Use the formula d = rt, and round your answer to the nearest tenth.

a. 564.0 mph c. 115.3 mph

b. 25.5 mph d. 70.4 mph

____ 13. The formula for the resistance of a conductor with voltage V and current I is r =V

I. Solve for V.

a. I = Vr c. V =I

r

b. V =r

Id. V = Ir

____ 14. Solve 4x − z = y for x.

a. x =

y + z

4c. x = y + z − 4

b. x =

y − z

4d. x =

y

4+ z

____ 15. Solve 3.8y +4

7x + 2 = 0 for y.

a. y = −10

19c. y = −

4

7x − 2

b. y = −20

133x −

10

19d. y = −

76

35x −

38

5

____ 16. Describe the solutions of 6 + y < 10 in words.

a. The value of y is a number less than or equal to 3.

b. The value of y is a number less than 4.

c. The value of y is a number equal to 3.

d. The value of y is a number greater than 4.

Name: ________________________ ID: A

3

____ 17. Graph the inequality m < –3.4.

a.

b.

c.

d.

____ 18. Write the inequality shown by the graph.

a. m < –3 c. m > –3

b. m ≤ –3 d. m ≥ –3

____ 19. To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n

represent the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will result in a swimmer making the team. Graph the solution.a. n ≤ 500

b. n ≥ 500

c. n > 500

d. n < 500

Name: ________________________ ID: A

4

____ 20. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can

spend the remainder of the money on music. Write an inequality to show how much he can spend on music. Then, graph the inequality.a. 180 + s ≤ 450; s ≤ 270

b. 450 + s < 180; s < 270

c. 180 + s ≥ 450; s ≥ 270

d. 450 + s > 180; s > 270

____ 21. Solve the inequality n + 6 < –1.5 and graph the solutions.

a. n < 4.5

b. n < –7.5

c. n < –7.5

d. n < 4.5

Name: ________________________ ID: A

5

____ 22. Carlotta subscribes to the HotBurn music service. She can download no more than 11 song files per week.

Carlotta has already downloaded 8 song files this week. Write, solve, and graph an inequality to show how

many more songs Carlotta can download.

a. s ≤ 3

b. s > 3

c. s ≥ 3

d. s < 3

____ 23. Denise has $365 in her saving account. She wants to save at least $635. Write and solve an inequality to

determine how much more money Denise must save to reach her goal. Let d represent the

amount of money in dollars Denise must save to reach her goal.

a. 365 + d > 635; d > 270 c. 365 + d = 635; d = 270b. 365 + d ≥ 635; d ≥ 270 d. 365 + d ≥ 635; d > 635

____ 24. Solve the inequality and graph the solution.

x + 12

5≤ 6

8

10

a. x ≤ 52

5

b. x ≥ 52

5

c. x ≥ 81

5

d. x ≤ 81

5

Name: ________________________ ID: A

6

____ 25. Solve the inequality x

8> 3 and graph the solutions.

a. x > 3

8

b. x > 24

c. x > 24

d. x > 24

____ 26. Solve the inequality 2m ≤ 18 and graph the solutions.

a. m ≤ 9

b. m ≤ 36

c. m ≤ 36

d. m ≤ 9

Name: ________________________ ID: A

7

____ 27. Solve the inequality z

−4 ≤ 2 and graph the solutions.

a. z ≥ –8

b. z ≤ –8

c. z ≤ 8

d. z ≥ 8

____ 28. Solve the inequality 2 f ≥ –8 and graph the solutions.

a. f ≥ –4

b. f ≥ 4

c. f ≤ 4

d. f ≤ –4

____ 29. Marco’s Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost

$2.50 each and he has $14.75 to spend, how many tickets can he buy?

a. 4 tickets c. 6 tickets

b. 0 tickets d. 5 tickets

____ 30. What is the greatest possible integer solution of the inequality 2.847x < 15.168?

a. 5.33 c. 4

b. 6 d. 5

Name: ________________________ ID: A

8

____ 31. Solve the inequality −n – 4 < 3 and graph the solutions.

a. n < –7

b. n < 1

c. n > –7

d. n > 1

____ 32. Solve the inequality z + 8 + 3z ≤ –4 and graph the solutions.

a. z ≥ 1

b. z ≤ 1

c. z ≥ –3

d. z ≤ –3

____ 33. A family travels to Bryce Canyon for three days. On the first day, they drove 150 miles. On the second day, they drove 190 miles. What is the least number of miles they drove on the third day if their average number of miles per day was at least 180?

a. 200 mi c. 540 mi

b. 180 mi d. 201 mi

Name: ________________________ ID: A

9

____ 34. Solve the inequality 6x < 3x + 15 and graph the solutions.

a. x > 5

b. x < –5

c. x > 3

d. x < 5

____ 35. Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 per

student. The Dino Discovery Museum simply charges $6 per student. For how many students will the Science Center charge less than the Dino Discovery Museum?

a. 132 or more students c. Fewer than 45 students

b. More than 45 students d. 132 or fewer students

____ 36. Solve the inequality and graph the solution.−3x + 2.5x ≤ 1.5(x + 4)

a. x ≥ 3

b. x ≤ −3

c. x ≥ −3

d. x ≤ 3

____ 37. Solve the inequality −2 k + 3� � < −2k − 7.

a. k < 1

4c. k < 3

1

4

b. All real numbers are solutions. d. no solutions

____ 38. Solve −0.25 + 1.75x < −1.75 + 2.25x.

a. 3 < x c. x < 3b. x < 6 d. x < 0.33

Name: ________________________ ID: A

10

____ 39. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if

there are at least 100 people on the plane. Write a compound inequality to show the possible number of people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions.

a. 100 ≥ n ≥ 240

b. 100 ≤ n ≤ 240

c. n ≤ 240

d. 100 < n < 240

____ 40. Solve the compound inequality 1 < 3x − 2 ≤ 10 and graph the solutions.

a. 1 < x AND x ≤ 4

b. 1 < x AND x < 4

c. 1 ≤ x AND x ≤ 4

d. 1 > x AND x ≥ 4

Name: ________________________ ID: A

11

____ 41. Solve and graph the compound inequality.

s + 4 < 1.5 OR 3 + s ≥ 7a. s < −2.5 OR s ≥ 4

b. s < −2.5 OR s < 4

c. s < −2.5 OR s < 4

d. s < −2.5 OR s ≥ 4

____ 42. Write the compound inequality shown by the graph.

a. x < −5 OR x > 3 c. x ≤ −5 OR x > 3b. x ≤ 3 AND x > −5 d. x ≤ −5 AND x > 3

____ 43. Which of the following is a solution of x − 6 < 6 AND x + 4 ≥ −1?

a. 2 c. 14

b. –6 d. 12

____ 44. Tell whether the ordered pair (5, –3) is a solution of the system −3x + 2y = −21

−x − y = −2

�

��

����������

.

a. yes b. no

Name: ________________________ ID: A

12

____ 45. Solve the system 3x + 4y = −36

−2x + 4y = −16

�

��

����������

by graphing.

a. (4, − 6) c. (4, 6)

b. (−4, 6) d. (−4, − 6)

____ 46. The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank

charges an annual fee of $17 plus $2.50 per game. For how many game rentals will the cost be the same at

both stores? What is that cost?a. 4 games; $27 c. 3 games; $22

b. 6 games; $38 d. 2 games; $16

Name: ________________________ ID: A

13

____ 47. If the pattern in the table continues, in what month will the number of sales of CDs and movie tickets be the

same? What number will that be?

Total Number Sold

Month 1 2 3 4

CDs 700 685 670 655

Movie tickets 100 145 190 235

a. Month 10; 550 c. Month 8; 580

b. Month 9; 580 d. Month 11; 550

____ 48. Solve 3x + y = −3

y = x + 5

�

��

����������

by substitution. Express your answer as an ordered pair.

a. ( 3, −2) c. (−4

3, 1)

b. (−2, 3) d. (−8

3, –3)

____ 49. Solve 4x − 4y = −16

x − 2y = −12

�

��

����������

by substitution. Express your answer as an ordered pair.

a. (8, –4) c. (–2, 4)

b. (4, 8) d. (4, –8)

____ 50. Janice is going on vacation and needs to leave her dog at a kennel. Nguyen’s Kennel charges $15 per day plus $20 for a processing fee. The Pup Palace Kennel charges $12 per day, and has a $35 processing fee. After how many days is the Pup Palace Kennel cheaper than Nguyen’s Kennel?

a. The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 15 days.

b. The Pup Palace Kennel is always cheaper than Nguyen’s Kennel.

c. The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 5 days.

d. The Pup Palace Kennel is never cheaper than Nguyen’s Kennel.

____ 51. Solve 2x − 3y = 11

3x + 3y = 9

�

�

�

�������������

by elimination. Express your answer as an ordered pair.

a. (–1, 4) c. (–2, –5)

b. (4, –1) d. (9, 2.33)

____ 52. Solve −7x + 5y = −5

−9x + 5y = 5

�

��

����������

by elimination. Express your answer as an ordered pair.

a. (0, –5) c. (0, –1)

b. (–5, –8) d. (–5, –4)

____ 53. Solve 2x − 5y = −7

5x − 3y = 11

�

��

����������

by elimination. Express your answer as an ordered pair.

a. (3, 4) c. (4

7,

8

5)

b. (3, 2) d. (4, 3)

Name: ________________________ ID: A

14

____ 54. At the local pet store, zebra fish cost $2.10 each and neon tetras cost $1.85 each. If Marsha bought 13 fish for

a total cost of $25.80, not including tax, how many of each type of fish did she buy?

a. 5 zebra fish, 8 neon tetras c. 8 zebra fish, 5 neon tetras

b. 7 zebra fish, 6 neon tetras d. 6 zebra fish, 7 neon tetras

____ 55. The sum of the digits of a two-digit number is 8. If the number is multiplied by 4, the result is 104. Write and solve a system of equations. Find the number.

a.x + y = 8

4(x + y) = 104

�

��

����������

The number is 35.

c.x + y = 8

4(2x + y) = 104

�

��

����������

The number is 18.

b.x + y = 8

4(10x + y) = 104

�

��

����������

The number is 17.

d.x + y = 8

4(10x + y) = 104

�

��

����������

The number is 26.

____ 56. Solve y = −x + 8

x + y = 7

�

��

����������

.

a. This system has infinitely many solutions.

b. This system has no solutions.

c. (1

2,

15

2)

d. (−1

2,

17

2)

____ 57. Solve y = 2x − 1

2x − y − 1 = 0

�

��

����������

.

a. This system has infinitely many solutions.

b. This system has exactly one solution.

c. This system has no solution.

d. (1, 1) and (0, 0)

____ 58. Elena and her husband Marc both drive to work. Elena’s car has a current mileage (total distance driven) of

9,000 and she drives 18,000 miles more each year. Marc’s car has a current mileage of 60,000 and he drives

7,000 miles more each year. Will the mileages for the two cars ever be equal? Explain.

a. No; The equations have equal slopes but different y-intercepts, so the lines do not intersect.

b. No; The equations have different slopes, so the lines do not intersect.

c. Yes; The equations have different slopes, so the lines intersect.

d. Yes; The equations have different y-intercepts, so the lines intersect.

____ 59. Tell whether (8, 5) is a solution of y > x + 7.

a. Yes, (8, 5) is a solution of y > x + 7.

b. No, (8, 5) is not a solution of y > x + 7.

____ 60. Tell whether (9, 2) is a solution of y < 4x + 1.

a. Yes, (9, 2) is a solution of y < 4x + 1.

b. No, (9, 2) is not a solution of y < 4x + 1.

Name: ________________________ ID: A

15

____ 61. Graph the solutions of the linear inequality −8x + 2y > −6.

a. c.

b. d.

Name: ________________________ ID: A

16

____ 62. Tony has $18 to buy apples and bananas for a fruit salad. Apples cost $2 per pound and bananas cost $1 per

pound. Write and graph an inequality to describe the situation. Then give two possible combinations of pounds of apples and bananas that Tony can buy.

Name: ________________________ ID: A

17

a. 2a + b ≤ 18; 2 pounds of apples and 12 pounds of bananas or 4 pounds of apples and 2

pounds of bananas.

b. 2a + b ≥ 18; 2 pounds of apples and 12 pounds of bananas or 4 pounds of apples and 2

pounds of bananas.

c. 2a + b ≤ 18; 2 pounds of apples and 18 pounds of bananas or 4 pounds of apples and 16 pounds of bananas.

Name: ________________________ ID: A

18

d. 2a + b ≥ 18; 2 pounds of apples and 18 pounds of bananas or 4 pounds of apples and 16

pounds of bananas.

____ 63. Write an inequality to represent the graph.

a. y > 2x + 3 c. y < 3x + 2

b. y ≤ 2x + 3 d. y < 2x + 3

____ 64. Tell whether (2, 7) is a solution of y ≥ 4x

y < x + 2

�

��

����������

.

a. No, (2, 7) is not a solution of the system.

b. Yes, (2, 7) is a solution of the system.

____ 65. A printing company will charge $6 plus $0.07 per page. Another company will charge $24 plus $0.04 per

page for the same project. For how many pages will the costs be the same regardless of which company is used?

a. 330 c. 600

b. 400 d. 1000

Name: ________________________ ID: A

19

____ 66. Solve –10(x – 1) = 10 – 10x.

a. no solution c. 0

b. –1 d. all real numbers

____ 67. Mrs. Nelson is buying folding chairs that are on sale for $10. If she has $50, which inequality can be solved to show the number of chairs c she can buy?

a. 10c ≤ 50 b. 10c ≥ 50

____ 68. Latisha is on page 30 of her book and reads 3 pages every night. Sal is on page 40 of the same book and reads

2 pages every night. How long will it take Latisha to be further in the book than Sal?a. 3 nights c. 15 nights

b. 11 nights d. 71 nights

____ 69. Which graph represents b ≥ 5.

a. c.

b. d.

____ 70. Which inequality is shown by the graph below?

a. x > –3 c. x < –3

b. x ≥ −3 d. x ≤ −3

____ 71. Which inequality represents the situation “no more than 160 students are in the freshman class”?

a. s > 160 c. s < 160

b. s ≥ 160 d. s ≤ 160

____ 72. Solve x + 7 > 2.

a. x > –5 c. x > 5

b. x < –5 d. x < 5

____ 73. Solve –4(x – 1) < 12.

a. x > –2 c. x > –3

b. x < –2 d. x < –3

____ 74. Solve 23− a > −3(2 − 6).

a. a < –6 c. a < –4

b. a > –6 d. a > –4

Name: ________________________ ID: A

20

____ 75. Solve by any method: −x + y = 1

x + y = 3

�

��

����������

.

a. (2, 1) b. (1, 2)

____ 76. Which term describes a system with exactly one solution?

a. consistent and independent c. inconsistent

b. consistent and dependent d. dependent

Numeric Response

1. The maximum speed of a greyhound is 153 miles per hour less than 3 times the maximum speed of a cheetah.

If a greyhound’s maximum speed is 42 miles per hour, what is the maximum speed of a greyhound? Check to make sure your answer is reasonable.

2. What is the least possible integer solution of the inequality 4.103x > 19.868?

3. A volleyball team scored 14 more points in its first game than in its third game. In the second game, the team

scored 28 points. The total number of points scored was less than 80. What is the greatest number of points the team could have scored in its first game?

Short Answer

1. Solve the equation.

10a – 35 = –8a + 1

Name: ________________________ ID: A

21

2. Solve the equation.

5(x + 1) = 5(x + 5) – 15

3. Describe the solutions of 1

3x ≥ 2 in words.

4. Graph the inequality.

k ≤ −1.

5. Graph the inequality.

w > 21

2

6. Write the inequality shown by the graph.

7. Citizens less than 18 years old are not allowed to vote. Define a variable and write an inequality for the ages of citizens who are not allowed to vote.

8. Solve the inequality.

x − 3

−7≤ 8

9. Solve the inequality.

−12 + 3x − 33< 18

10. Tell whether (–5, –6) is a solution of x − 2y = 7

y − x = −1

�

��

����������

.