testbanktop.comtestbanktop.com/wp-content/uploads/2016/12/downloadable-solution... · m-6...

M-5

Mini-Lecture 2.1 Linear Equations in One Variable

Learning Objectives:

1. Solve linear equations using properties of equality. 2. Solve linear equations that can be simplified by combining like terms. 3. Solve linear equations containing fractions or decimals. 4. Recognize identities and equations with no solution. 5. Key vocabulary: equation, solution, equivalent equation, contradiction, identity.

Examples:

1. Solve each equation and check.

a) 5 7x − = b) 3 15x + = c) 3 15x− = d) 34

x =

2. Solve each equation and check. a) 4 2 6 3x x− = + b) 5 4 10 3y y− = + c) 3(2 4) 9 3x x+ = − d) 2(3 1) 5( 4)n n n− − − = − −

3. Solve each equation and check.

a) 1

3 2 4

x x+ = b) 2

55 3

x x− = c) 2

35 10

r r− =

d) 28 4

3

xx

− = e) 2 6

1 25

yy

− = − f) 3.4(2 5) 0.2(2 5)x x+ = − +

4. Solve each equation.

a) 2( 6) 12 2x x+ = + b) 4( 5) 3 5( 2)x x x+ + = + −

Teaching Notes:

• Encourage students to check their solutions. • Some students prefer to always end up with the variable on the left, while others prefer to always end

up with a positive coefficient in front of the variable. • Some students try to subtract the coefficient from a variable instead of dividing it off. • Refer students to the Addition/Multiplication Property and Solving a Linear Equation in One

Variable charts in the text.

Answers: 1a){12}, b){12}, c){-5}; d) {12} 2a) {8}, b) {7}, c) {5}, d) {-9}; 3a) 3

10⎧ ⎫⎨ ⎬⎩ ⎭

, b) {75}, c) {10}, d) {4}, e) 11

12⎧ ⎫⎨ ⎬⎩ ⎭

,

f) {-2.5}; 4a) {x|x is a real number}, b) ∅

Copyright © 2009 Pearson Education, Inc., publishing as Pearson Prentice Hall

M-6

Mini-Lecture 2.2 An Introduction to Problem Solving


1. Write algebraic expressions that can be simplified. 2. Apply the steps for problem solving. 3. Key vocabulary: consecutive integers, complementary angles, supplementary angles.

Examples:

1. Write the following as algebraic expressions. Then simplify.

a) The sum of three consecutive integers if the first integer is x. b) The perimeter of a rectangle with length x and width x – 7. c) The total amount of money (in cents) in x quarters, 5x dimes, and (3x-1) nickels.

2. Solve using the General Strategy for Problem Solving.

a) Number Problem One number is two times another number. The sum of the numbers is 90.

What are the two numbers? b) Number Problem Three times the difference of a number and 5 is the same as 1 increased by

five times the number plus twice the number.

c) Age Problem Today Henry is 7 years older than twice his age of 23 years ago. Find Henry’s age today.

d) Car Rental A car rental agency advertised renting a luxury, full-size car for $19.95 per day and

$0.29 per mile. If you rent this car for 5 days, how many whole miles can you drive if you only have $200 to spend?

e) Carpentry A 7-ft. board is cut into 2 pieces so that one piece is 3 feet longer than 3 times the

shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

f) Unknown Sides A triangle has sides measuring 2.5x cm, 3x cm, and (2x + 3) cm. It’s perimeter measures 60 cm. Find the measures of the sides.

g) Unknown Angles Two angles are complementary if their sum is 90°. If the measure of the first

angle is x°, and the measure of the second angle is (3x – 2)°, find the measure of each angle.

h) Lay-offs A major car manufacturer announced it would lay off 17,000 employees worldwide. This is equivalent to 20% of its work force. Find the size of the work force prior to lay-offs.

Teaching Notes:

• Many students have difficulty with word problems. • Encourage students to draw and label diagrams when appropriate. • Some students need to see several examples of consecutive or consecutive odd/even integers. • Refer students to the General Strategy for Problem Solving chart in the text.

Answers: 1a) x+x+1+x+2=3x+3, b) 4x-14, c) 90x-5; 2a) 30,60, b) -4, c) 39, d) 345 miles, e) 1 foot, 6 feet, f) 19 cm, 22.8 cm, 18.2 cm, g) 23°, 67°, h) 85,000 employees


M-7

Mini-Lecture 2.3 Formulas and Problem Solving


1. Solve a formula for a specified variable. 2. Use formulas to solve problems. 3. Key vocabulary: formula.

Examples:

1. Solve each equation for the specified variable.

a) M kt= for t b) 2C rπ= for r c) 2 2 2a b c+ = for a2

d) 4 5 16x y+ = for y e) 2 2P l w= + for l f) 5

( 32)9

C F= − for F

2. Solve. Round all dollar amounts to two decimal places.

a) Volume Find the volume of a rectangular crate with dimensions 3 ft by 4 ft by 8 ft. b) Distance Sheranda drives at a constant 65 miles per hour. How far will she travel in 4 hours?

c) Compound Interest Emmanuel puts $5010 at 9% compounded semiannually for 12 years. What is the value of his account at the end of the 12 years?

d) Circle Crystal is making a cover for a round table that has a diameter of 46 inches. How much fabric will she need if she wants the cover to fit exactly, with no material hanging off? (Use 3.14 for π and round to two decimal places.)

e) Office Rental An accountant rents office space. He is charged $2040 per month for a rectangular office that measures 17 ft by 20 ft. How much is he paying each month in rent per square foot?

f) Temperature Michael’s cousin Luke was visiting from Montreal during the summer. On a news report Luke heard that the temperature in Montreal that day was 98°F. He was used to hearing temperature in degrees Celsius. What is 98°F in degrees Celsius?

g) Triangle A triangular piece of wood needs to be varnished. The base of the triangle is 3 meters and the height is 13 meters. How many cans of varnish will be needed if each can covers 10 square meters?

Teaching Notes:

• Some students are very confused by solving for a variable when other variables are present. • Many students benefit from seeing a parallel example with numbers instead of variables. For

example, next to 1a) solve: 6 = 3t • Encourage students to draw and label diagrams when appropriate. • Refer students to the Formula and Solving an Equation for a Specified Variable charts in the text.

Answers: 1a) M

tk

= , b) 2

Cr

π= , c) 2 2 2a c b= − , d)

16 4

5

xy

−= , e) 2

2

P wl

−= , f) 9

325

F C= + ; 2a) 96 cubic feet,

b) 260 miles, c) $14,408.83, d) 1,661.06 square inches, e) $6.00 per square foot, f) 36.67°C, g) 2 cans


M-8

Mini-Lecture 2.4 Linear Inequalities and Problem Solving


1. Use interval notation. 2. Solve linear inequalities using the addition property of inequality. 3. Solve linear inequalities using the multiplication property and the addition properties of inequality. 4. Solve problems that can be modeled by linear inequalities. 5. Key vocabulary: greater than (or equal to), less than (or equal to), solution set, interval notation.

Examples:

1. Graph the solution set of each inequality on a number line and then write it in interval notation.

a) { | 3}x x > b) { | 2}x x < − c) { | 4.2 }x x− ≥ d) { | 3 0}x x− < ≤

2. Solve. Graph the solution set and write it in interval notation.

a) 2 6x + ≤ b) 10 9 3x x< + c) 5 5 4 5x x− ≥ −

3. Solve. Graph the solution set and write it in interval notation.

a) 1

22

x ≥ b) 2 7.2x > − c) 3 6x− ≤

d) 2)2(2 +≥+ xx e) 0.3(6 1) 1.4( 3) 0.1x x− < − − f) 5 3

6 4 3

x− >

4. Solve. Show your answer as an inequality. A salesperson earns $2000 a month plus a commission of 20% of sales. Find the minimum amount of sales needed to receive a total income of at least $6000.

Teaching Notes:

• Some students are very confused by solving for a variable when other variables are present. • Many students forget to reverse the direction of the inequality symbol when necessary. • Some students prefer to move the variable in such a way that it has a positive coefficient if possible. • Refer to the end-of-section exercises for application problems. • Refer students to the Addition/Multiplication Property of Inequality and Solving a Linear Inequality in One Variable charts in the text.

Answers: (graph answers at end of mini-lectures) 1a) (3, )∞ , b) ( , 2)−∞ − , c) ( , 4.2]−∞ − , d) ( 3,0]− ; 2a) ( ,4]−∞ ,

b) ( ,3)−∞ , c) [0, )∞ ; 3a) [4, )∞ , b) ( 3.6, )− ∞ , c) [ 2, )− ∞ , d) 2x ≤ − , e) 10x < − , f) 4

1<x ; 4) { / $20,000}x x ≥


M-9

Mini-Lecture 2.5 Compound Inequalities


1. Find the intersection of two sets. 2. Solve compound inequalities containing “and”. 3. Find the union of two sets. 4. Solve compound inequalities containing “or”. 5. Key vocabulary: and, or, intersection, union.

Examples:

1. If { | is an even integer}A x x= , { | is an odd integer}B x x= , {1,2,3,4}C = , and {3,4,5,6}D = , list

the elements of each set. a) C D∩ b) B C∩ c) A B∩

2. Solve each compound inequality by graphing the solution on a number line.

a) 1 and 3x x≤ ≥ − b) 1 and 4x x< > c) 3 and 2x x≥ − > Solve each compound inequality. Write solutions in interval notation. d) 3 4 and 5 2 8x x+ ≥ − ≥ e) 5 15 and 15 10x x− < − − < −

f) 4 1 2x− ≤ + ≤ − g) 2

3 1 13

x− < − < h) 3 4

1 15

x− +− ≤ ≤

3. If { | is an even integer}A x x= , { | is an odd integer}B x x= , }6,5,4,3{=C and }7,6,5,4{=D , list the elements of each set. a) CB ∪ b) C D∪ c) A D∪

4. Solve each compound inequality by graphing the solution on a number line.

a) 3 or 3x x≥ − ≤ b) 1 or 1x x< − < c) 2 or 3x x≥ − ≤ − Solve each compound inequality. Write solutions in interval notation. d) 10 20 or 3 4 2x x− ≤ − ≥ e) 8 1 or 5 15x x+ < − > − f) 6( 2) 12 or 4 10x x− ≥ − − ≤

Teaching Notes:

• In problems 2a-c) and 4a-c), show students how each inequality can be graphed separately on its own number line. Then the solution graph is the intersection (or union) of the individual graphs.

Answers: (graph answers at end of mini-lectures) 1a) {3,4}, b) {1,3}, c) ∅ ; 2a) [-3,1], b) no solution, c) (2, )∞ , d)

[2, )∞ , e) (3,5), f) [-5,-3], g) (-3,3), h) 1

,33

⎡ ⎤−⎢ ⎥⎣ ⎦; 3a) {x|x is an odd integer, x=4, x=6, b) {1,2,3,4,5,6},

c) {x|x is an even integer, x=3, x=5; 4a) all real numbers, b) ( ,1)−∞ , c) ( , 3] [ 2, )−∞ − ∪ − ∞ , d) [ 2, )− ∞ , e) ( , 9) ( 3, )−∞ − ∪ − ∞ , f) [ 6, )− ∞


M-10

Mini-Lecture 2.6 Absolute Value Equations


1. Solve absolute value equations.

Examples:

1. Solve.

a) | | 6x = b) | | 6x = − c) | 3 | 9.3m = d) 6 | | 7 5x − =

e) | 4 | 9x + = f) 2 13

x − = g) | 5 | 0x = h) | 2 3 | 9 4n + + =

i) 2 | 1| 15 20x − + = j) | 5 9 | | 4 |x x+ = + k) 1 2

3 12 3

x x+ = −

Solve each equation for x.

l) | | 2x = m) | 3 | 15x = n) | | 3 7x − = − o) | 4 1| 9 11x − + =

Teaching Notes:

• Refer students to the Absolute Value Property and Solving Absolute Value Equations charts in the text.

Answers: 1a) {6,-6}, b) ∅ , c) {3.1,-3.1}, d) {-2,2}, e) {-13,5}, f) {3,9}, g) {0}, h) ∅ , i) 3 7

,2 2

⎧ ⎫−⎨ ⎬⎩ ⎭

, j) 13 5

,6 4

⎧ ⎫− −⎨ ⎬⎩ ⎭

, k)

1224,

7⎧ ⎫−⎨ ⎬⎩ ⎭

, l) {-2,2}, m) {5,-5}, n) ∅ , o) 1 3

,4 4

⎧ ⎫−⎨ ⎬⎩ ⎭


M-11

Mini-Lecture 2.7 Absolute Value Inequalities


1. Solve absolute value inequalities.

Examples:

1. Solve. Graph the solution set.

a) | | 3x ≤ b) 3x ≥ c) | | 3x < − d) | | 3x > −

e) | 3 | 7x + < f) | | 4 8x + ≤ g) 3

15

x − < h) | 6 3 | 4x− <

i) | 5 | 8x − ≥ j) | | 6 7x + > k) | 9 4 | 3 2x+ − > − l) 11

27

x+ ≥

Solve each inequality for x.

m) | | 4x < n) | 8 2 | 0x+ ≥ o) | 2 | 8x − ≥ p) 1

3 23

x − <

Teaching Notes:

• Most students need to see the solutions to 1a-d) on a number line in order to visualize the solution set. For the rest of the problems in 1 they can go right to the method shown in the solving Inequalities chart in the text.

• Refer students to the Absolute Value Property and Inequalities charts in the text.

Answers: (graph answers at end of mini-lectures) 1a) [-3,3], b) ( , 3] [3, )−∞ − ∪ ∞ , c) ∅ , d) {all real numbers}, e) (-10,4),

f) [-4,4], g) (-2,8), h) 2 10

,3 3

⎛ ⎞⎜ ⎟⎝ ⎠

, i) ( , 3] [13, )∞ − ∪ ∞ , j) ( , 1) (1, )−∞ − ∪ ∞ , k) 5

, ( 2, )2

⎛ ⎞−∞ − ∪ − ∞⎜ ⎟⎝ ⎠

, l) ( , 25] [3, )−∞ − ∪ ∞ ;

m) (-4,4), n) {all real numbers}, o) ( , 6] [10, )−∞ − ∪ ∞ , p) (3,15)


E-10

Additional Exercises 2.1 Form I

Solve each equation and check.

1. 4 3 5x

2. 0.2 0.4 1.0x

3. 4 1 5 1y y

4. 2( 1) 4x

5. 62

x

6. 3 2 5 2x x

7. 5 1 4 5x x

8. 3 2( 3) 4( 3)y y y

9. 4 2

3 3 3

x x

10. 0.6( 1) 2(0.2 0.1)x

11. 5 4 2

9 9 3x

12. (1 2 ) ( 2)

5 2 10

x x x

13. 3 1 2

28 2 4

x x

Solve each equation.

14. 2(2 3) 3( 6)x x x

15. 3( 2) 2 6x x x

Name ________________________

Date _________________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-11

Additional Exercises 2.1 Form II


1. 3 5 7x

2. 0.2 0.3 1.1x

3. 8 7 4 5y y

4. 3( 5) 12x

5. 4 122

x

6. 5 3 3 5x x

7. 2 3 1 5 3x x

8. 4 2( 3) 5( 3)x x x

9. 2 2

9 3 9

x x

10. 1.6(2 1) 2(0.4 0.7)x x

11. 1 8 1

19 9 3

x x

12. 1 2 5

3 5 3

x x

13. 5 3( 2)

28 4

x xx


14. 4( 3) 8( 2) 4x x x

15. 7( 1) 3 3 4( 2) 2x x x

Name _________________________

Date _________________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-12

Additional Exercises 2.1 Form III


1. 1 6 11x

2. 1.4 2.5 1.9x x

3. 6 1 7 1y y

4. 4(3 1) 6x

5. 2

205

x

6. 5 7 3 9x x

7. 7 11 2 2 8x x

8. ( 11) 5 (2 9)y y y

9. 3 2 9

7 7 14

x x

10. 0.07 0.11 3.6(1 )x x x

11. 6 1 5

16 2 4 8

x x x

12. 3 3 3 2

2 76 4

x xx

13. (1 4 ) (3 3) (2 1)

2( 3)5 3 5

x x xx


14. 4( 3 1) 22 6 3(2 6)x x x

15. 9(2 1) 4 12 5 7x x x x

Name _________________________

Date _________________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-13

Additional Exercises 2.2 Form I

Write the following as algebraic expressions. Then simplify.

1. The perimeter of a square with sides of length b.

2. The sum of three consecutive integers if the first is n.

3. The total amount of money (in cents) in 3x nickels and

2x dimes.

Solve.

4. A bicycle costs $91.80 including tax. If the tax rate is 8%,

find the price of the bike before taxes.

5. 45% of the students in a class of 40 are girls. How many

students in the class are girls?

6. Twice a number is 6 more than the number. Find the

number.

7. One number is 13 more than another number. If the sum

of the two numbers is 15, find the two numbers.

8. The length of a square garden is twice a number. If the

perimeter of the garden is 36, find the number.

9. The perimeter of a rectangular window is 96. If the length

is twice the width, find the length and the width.

10. One angle of two complementary angles is 20º more than

the other angle. Find the measures of the two angles.

11. A right triangle has three angles: a right angle, another

angle, and an angle with twice the measure of the second

angle. Find the measures of the angles of the triangle.

12. One angle of two supplementary angles is four times the

other angle. Find the measures of the two angles.

13. The sum of three consecutive numbers is 39. Find the

three numbers.

14. The sum of two consecutive odd integers is 96. Find the

two integers.

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________


E-14

Additional Exercises 2.2 Form II


1. The perimeter of a square with sides of length 3x.

2. The sum of three consecutive integers if the first is n + 2.

3. The total amount of money (in cents) in 3x nickels,

4x dimes, and 3x quarters.

Solve.

4. A computer costs $1389.93 including tax. If the tax rate is

7%, find the price of the computer before taxes.

5. 35% of the students in a school of 2060 are freshmen.

How many students in the school are freshmen?

6. Three more than twice the sum of 7 and a number is 25.

Find the number.

7. One number is 3 times another. If the difference of the

numbers is 36, find the two numbers.

8. The length of a rectangular garden is four feet more than

twice its width. If the perimeter of the garden is 100 feet,

find the length and width of the garden.

9. The lengths of the sides of a triangle are consecutive

integers. If the perimeter of the triangle is 111, find the

lengths of the sides.

10. One angle of an isosceles triangle is three times the

measure of each of the other two angles. Find the

measures of the angles.

11. One of the non-right angles of a right triangle has a

measure 20º more than twice the measure of the other

non-right angle. Find the measures of the angles of the

right triangle.

12. One angle of two supplementary angles is 4º more than

one third of the other angle. Find the measures of the two

angles.

13. Regi received a 3.5% raise, which raised his yearly

income by $910. What is his new income?

14. The difference of a number and its opposite is 28. Find the

number.

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________


E-15

Additional Exercises 2.2 Form III


1. The perimeter of a square with sides of length 2x − 1.

2. The sum of three consecutive odd integers if the first is

4 + s.

3. The total amount of money (in cents) in 3x − 1 nickels,

2x – 3 dimes, and x + 1 quarters.

Solve.

4. A laptop computer costs $1,581 including tax. If the tax

rate is 8%, find the price of the laptop, to the nearest

hundredth, before taxes.

5. About 19% of the students in a school of 12,918 are

seniors. How many students in the school are seniors?

Round your answer to the nearest whole number.

6. Three times a number is 3 less than twice the sum of 5 and

the number. Find the number.

7. One number is 13 more than the product of 9 and another

number. If the sum of the two numbers is 103, find the

two numbers.

8. The length of a rectangular garden is 4 yards more than

twice the width. If the perimeter of the garden is 51 yards,

find its length and width.

9. The sum of two consecutive numbers is 6 more than three

times their difference. Find the two numbers.

10. One angle of two complementary angles is 18º more than

the twice the sum of other angle and 5°. Find the measures

of the two angles.

11. The difference of the two non-right angles of a right

triangle is twice the smaller non-right angle. Find the

measures of the two angles.

12. One angle of two supplementary angles is four times the

other angle. Find the measures of the two angles.

13. A student spent $583.15 on textbook purchases. If the tax

rate is 7%, what was the price of the textbooks before tax?

14. The sum of three consecutive odd integers is 7 more than

twice the smallest integer. Find the integers.

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________


E-16

Additional Exercises 2.3 Form I Solve each equation for the specified variable.

1. A = lw for w

2. 2m n s for s

3. 3 4 7x y for y

4. 1 1 2 2t r t r for

2t

5. Fd

Pt

for F

6. 21

2V h for h

7. 2A r rS for S

8. 2 ( )A r r h for h

9. 2P I R VI for V

10. 2 3 1T ms s for s

Solve.

11. A principal of $10,000 is invested in an account paying an

annual percentage rate of 5%. Round all dollar amounts to

two decimal places. Find the amount in the account after 10

years if the account is compounded n times a year.

a. n = 4 b. n = 12

12. A record low temperature for Honolulu, Hawaii is 53F.

Write 53F as degrees Celsius. Use the formula

5

9( 32)C F . Round to the nearest degree.

13. It is 470 miles from Oklahoma City, Oklahoma to

Memphis, Tennessee. Find how long it takes to drive

round-trip if the average speed is 65 mph. Round to the

nearest minute.

14. Find the volume of a ball with radius 6 inches. Use the

formula 34

3V r . Round to the nearest whole number.

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11a. _______________________

11b. _______________________

12. ________________________

13. ________________________

14. ________________________


E-17

Additional Exercises 2.3 Form II Solve each equation for the specified variable.

1. C = D for D

2. v s gt for s

3. 5 2 11x y for y

4. 1 1 2 2PV PV for

2P

5. 2

2

WvKE

g for W

6. 22

3V r h for h

7. ( )2

nS a k for n

8. ( )E I r R for r

9. 21

2E mgh mv for h

10. 5 3K ab b a for a

Solve.

11. A principal of $8000 is invested in an account paying an

annual percentage rate of 5%. Round all dollar amounts to

two decimal places. Find the amount in the account after 2

years if the account is compounded

a. semiannually b. monthly

12. A package of vinyl floor tiles contains 45 one-foot-square

tiles. Find how many packages should be bought to cover

the rectangular floor of an outlet store that is 120 feet by

90 feet.

13. A gallon of paint can cover 400 square feet. To the nearest

half gallon, find how much paint will be needed to paint

two coats on the walls and ceiling of a room that is 20 feet

long, 18 feet wide, and 8 feet high.

14. Jamal wants to collect rainwater in a cylindrical barrel that

has a diameter of 3 feet and height of 5 feet. How much

water could it hold in cubic feet? Use the formula 2V r h . Round to two decimal places.

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11a. _______________________

11b. _______________________

12. ________________________

13. ________________________

14. ________________________


E-18

Additional Exercises 2.3 Form III Solve each equation for the specified variable.

1. m

DV

for V

2. 6 1g ts for t

3. 12 5 9x y for y

4.

1 2 2 1PT kPT for k

5. 2mv

Fgr

for g

6. 1 2

1( )

2A h b b for h

7. ( 1)l a n d for d

8. 1

rl aS

r

for a

9. 21

2E mgh mv for m

10. 1 1 1

a b c for c

Solve.

11. A principal of $9535 is invested in an account paying an

annual percentage rate of 4.5%. Round all dollar amounts

to two decimal places. Find the amount in the account

after 5 years if the account is compounded

a. quarterly b. monthly

12. Michaela can have unlimited on-line services for a flat fee

of $20 per month or limited access for 10¢ per minute.

Find the amount of time on-line for which the unlimited

access plan costs the same as the limited-access plan.

13. Sally has scores of 88, 92, 80, and 96. Find the score she

must make on the next exam to have an average of 90.

14. A company finds that the cost C to produce x items is

C = 10,025 + 1.09x, while the revenue is R = 6.42x. Find

the break-even point. (Cost equals revenue at the break-

even point.) Round to the nearest whole number.

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11a. _______________________

11b. _______________________

12. ________________________

13. ________________________

14. ________________________


E-19

Additional Exercises 2.4 Form I Graph the solution set of each inequality and write it in interval

notation.

1. | 3x x

2. |3x x

3. | 2 0x x

Solve. Graph the solution set and write it in interval notation.

4. x – 4 –7

5. 2.5x > –10

6. 3x < 2x – 6

7. 9x – 5 8x + 3

Solve. Write the solution set using interval notation.

8. 3 1 13x

9. 5(3 1) 2(6 8)x x

10. 2( 3) 6 2x x

Solve.

11. A custodian must move a shipment of books from the first

floor to the sixth floor. The elevator’s weight limit is 900

pounds. If the custodian weighs 160 pounds and each box

of books weighs 37 pounds, find the maximum number of

boxes the custodian can move on the elevator at one time.

Name ______________________

Date _______________________

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


E-20

Additional Exercises 2.4 Form II Graph the solution set of each inequality and write it in interval

notation.

1. | 2.5x x

2. | 1x x

3. | 1 4x x


4. –4x + 7 < –9

5. 3x – 5 > 6x + 4

6. 3.2 9.6x

7. 2(x - 1) 3(x – 2)


8. 38

( 2) (2 )5

x x

9. 2( 5) 6 5( 3)x x x

10. 4(1 2 ) 3( 3) 5 1x x x

Solve.

11. To receive an A in a course, Twan must have an average

of 90 or above. If Twan’s first four exam grades are 96,

90, 87, and 95, what is the minimum grade Twan can

receive on the last exam to get an A in the course?

Name ______________________

Date _______________________

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


E-21

Additional Exercises 2.4 Form III Graph the solution set of each inequality and write it in interval

notation.

1. |1.5x x

2. |0 2.75x x

3. | 2 5x x


4. 2 4

( 6) ( 4)3 5

x x

5. 2 1 3 2

15 2

x xx

6. 1.5 – 0.6x < – 0.7

7. 2 4 3 1

5 5 10 5x x


8. 1

3

4( 3) ( 6)

3x x

9. 8x – 7(1 + x) 3(x – 2) + 2x

10. 3

(2 5 ) 2(2 5) ( 7)5

x x x

Solve.

11. For Brooke’s cookie company to make a profit, her

revenue R must be greater than her cost C. Her weekly

cost equation is C = 1.7x + 1525 and her weekly revenue

equation is R = 4.2x, where x is the number of packages o

cookies produced and sold in a week. How many packages

of cookies must Brooke’s company produce and sell in a

week to make a profit?

Name ______________________

Date _______________________

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


E-22

Additional Exercises 2.5 Form I If A = {0, 3, 6, 9, 12, 15}, B = {–12, –6, 0, 6, 12}, and C = {0}, list

the elements of each set.

1. A B

2. A C

3. A C

4. A B

Solve each compound inequality. Graph the solution set, and write it in interval notation.

5. x < 2 and x > 1

6. x − 3 < 2 and x > −1

7. x > −2 and x < 1

8. 2x + 3 < 1 or x − 5 > 4

Solve each compound inequality. Write the solution set in interval

notation. 9. x + 1 > –2 and x + 2 < 3

10. x – 6 4 and 2x – 3 1

11. –1 2x + 3 < 7

12. −11 3x − 2 < 7

13. 4 2( 3) 0x

14. 1 2 1 5x

15. 5x – 3 7 or 2 + x > 5

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-23

Additional Exercises 2.5 Form II If A = {−1, 0, 2, 3, 7, 11}, B = {–5, 7}, and C = {x| x is an even integer}, list the elements of each set

1. A B

2. A B

3. B C

4. B C


5. x < 4 and x > –1

6. 7x < 2 and x < 0

7. x < 3 and 3x > –2

8. 5x – 1 < 4 or 4x + 1 > 5


notation.

9. 3x – 1 < 13 and 6x > 25

10. 4x – 4 > –1 or x + 7 < 2 11. 4x – 2 < 12 and x + 4 > –9

12. 4 < 2x + 3 < 9

13. –2 4x – 5 < 7

14. 4( 1)

0 123

x

15. 0.3 0.5 2.1 11.2x

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-24

Additional Exercises 2.5 Form III If A = {x| x is an even integer}, B = {x| x is an odd integer}, and

C = {x| x < 0}, list the elements of each set.

1. A B

2. A B

3. B C

4. B C


5. x < 3 and x > −3

6. x < 2 and x < 0

7. x < −2 and x > 2

8. x < −3 or x > 3


notation. 9. 6x – 5 < 1 and – x > 3

10. 2 < x + 7 and x – 4 > 3

11. 4x – 3 > 13 or – x > 2

12. −4 < 2x + 7 < 3

13. 1 5

2 13 9

x

14. 3(2 5)

2 137

x

15. 1.7 2.8 5.3 4.1x (Round to the nearest tenth)

Name ________________________

Date _________________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-25

Additional Exercises 2.6 Form I Solve each absolute value equation.

1. 3x

2. 3 7x

3. 2 8x

4. 5 3 2x

5. | | 4x

6. 5 3 0x

7. 4 2 0x

8. 7 2 5 3x

Solve.

9. 3 2 4x x

10. 3 1 2x x

11. 2 | 1| 2 6x

12. 2 3 3x x

13. 4 2 3 2x x

14. 1 3 3x x

15. 2 2 1x x

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-26

Additional Exercises 2.6 Form II Solve each absolute value equation.

1. 9x

2. 1 5x

3. 4x

4. 5

72 2

x

5. 8 19 0x

6. 6 1 7x

7. |5 | 8 6x

8. 4 11 3 2x

9. 5 4 2x

Solve.

10. 4 1 3x x

11. 7 2 4 3x x

12. 4 | 5 | 10 18x

13. 1 3

1 32 2

x x

14. 5 3 3 2x x

15. 4 7 4x x

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-27

Additional Exercises 2.6 Form III Solve each absolute value equation.

1. 5x

2. | 2 | 7x

3. 6

1 05

x

4. 1 3 2 1x

5. 2 15 5 3x

6. 5 4 3 3x

7. 7 3 4x

8. 2 13 5 3x

Solve.

9. 5 3 2 3x x

10. 8 14 7 23x x

11. 1 3

4 52 4

x x

12. 2 1

1 33 2

x x

13. 1 2

6 82 3

x x

14. 3 1

2 55 4

x x

15. 2 4

3 45 7

x x

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________

12. ________________________

13. ________________________

14. ________________________

15. ________________________


E-28

Additional Exercises 2.7 Form I Solve each inequality. Then graph the solution set, and write it in

interval notation.

1. 5x

2. 4 3x

3. 4 6x

Solve each inequality. Graph the solution set, and write it in

interval notation.

4. 2x

5. 7 4x

6. | 3 1| 5 2x

Solve each equation or inequality for x.

7. 4 2 10x

8. 1 2 1x

9. 5 15 0x

10. 3

5 62

x

11. 2 1

42

x

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________


E-29

Additional Exercises 2.7 Form II Solve each inequality. Then graph the solution set, and write it in

interval notation.

1. 2 5x

2. 2 4 3x

3. 4 1 3x


interval notation.

4. 2 4x

5. 2 3 5x

6. | 3 2 | 2 6x


7. 2 1 6 8x

8. 2 3 4 2x

9. 4 2x

10. 4 4

85

x

11. 3 5 1x

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________


E-30

Additional Exercises 2.7 Form III Solve each inequality. Then graph the solution set, and write it in

interval notation.

1. 2 6x

2. 5 3 4x

3. 7 4 4 5x


interval notation.

4. 5 1 0x

5. 11 9 1x

6. | 3 2 | 1 5x


7. 2 5 3 10x

8. 2 3 4 2x

9. 4 4

85

x

10. 7 1

26

x

11. 7 3

2 112

x

Name ______________________

Date _______________________

1. ________________________

2. ________________________

3. ________________________

4. ________________________

5. ________________________

6. ________________________

7. ________________________

8. ________________________

9. ________________________

10. ________________________

11. ________________________


Name: Date: Instructor: Section:

A- 6

Section 2.1 Linear Equations in One Variable Objective: Solving and checking linear equations. Suggested Format: Small group of 3 or 4 Time: 15 minutes Work each equation and check your solution in the original problem. Solve Check 1. ( )2 6 4 3x x− = −

2. ( ) ( )3 4 2 3 2 3 4 1x x x− + − = + +

3. ( )1 2 3 2 1x x− = − + (Try x = 3 to see if you get a true statement)

(Try a number you picked to see if you get a true statement.)

4. Are there problems where there is no solution? How do you identify them?



A- 7

Section 2.2 An Introduction to Problem Solving Objective: Apply problem-solving techniques to real-life problems.. Suggested Format: Small group of 3 or 4 Time: 20 minutes Rates for the “Terminor Phone Company”

Basic Plan Security Plan Monthly Access Fee: $14.95 $36.95 Airtime (per minute):

Peak: $0.69 $0.39 Off-Peak: $0.39 $0.39

The Problem: Suppose you are considering signing up for cell phone service with Terminor Phone Company which offers two calling plans. The Security Plan has a higher monthly fee, but a lower rate for peak hours. The Security Plan gives 30 minutes of free calls during peak hours each month. You must decide which plan to sign up for. The Question: How many minutes per month would you have to use in order to “break even,” that is for the costs of the two plans to be equal. Assume that you talk only during peak hours (since off-peak hours are the same cost for each plan). 1. Fill in the blanks with your “break-even” equation written first in words.

______________________________ = ___________________________

2. Let x be the unknown in this situation. What will x represent? 3. Write your equation using the data and your variable x. Then solve your equation.

______________________________ = ___________________________ 4. Describe your results. Which plan is better if you talk 30 minutes a month?



A- 8

Section 2.3 Formulas and Problem Solving Objective: Practice problem solving skills with a simple formula. Suggested Format: Small group of 3 or 4 Time: 15inutes NOTE TO THE INSTRUCTOR: You will want to bring in various round objects, string, and rulers (or tape measures) for each group. Examples of objects are canned goods, jars, round trash cans. You will need three round objects for each group. Circumference and Radius The formula 2C rπ= expresses the relationship between the circumference, C, of a circular object and the radius, r, of that object. 1. Measure around the outside of the object with your string or tape measure. Lay the

string on the tape measure and approximate the circumference of the object. Use the formula 2C rπ= and solve for the value of the radius. Use 3.14 for π . Fill in the table for each object.

Circumference r

Object 1

Object 2

Object 3

2. Measure across the top of the cylindrical object. Divide by 2 to get the radius. See if

this is approximately the same as you obtained in part 1. diameter r

Object 1

Object 2

Object 3

3. If you were assigned the job of finding the radius of many objects using the

circumference, it would save your time if solved for r. Solve 2C rπ= for r.



T- 19

Chapter 2 Test Form A


1. ( )3 5 4 6x x+ = − − 1. ____________________

2. 4 3 7 6m m− = + 2. ____________________

3. ( ) ( )3 5 3 4 3x x x− + + = − 3. ____________________

4. ( ) ( )5 2 3 2 4 6 4 8y y− − = − + 4. _____________________

5. 2 14 2

x x+ = + 5. ____________________

6. ( ) ( )3 5 4 12 5

5 4 10

x xx + −+− = 6. ____________________

7. 3 2

42

m −= 7. ____________________

8. ( )3 2 8 6x − − = − 8. ____________________

9. 3 4 1n n− = − 9. ____________________

10. ( )5 1 5 1y y− = − + 10. ____________________

Solve for the indicated variable.

11. 4 2 6x y+ = , for y 11. ____________________

12. 1 5 2

x y z+ = , for y 12. ____________________

13. ( )2

3 12

a ba

+= − , for a 13. ____________________



T- 20

Chapter 2 Test Form A cont’d

Find the solution for each inequality. Write the answer in interval notation.

14. ( )2 6 3 7x x− < + 14. ____________________

15. 2 3 7x − ≤ 15. ____________________

16. 3 5 19x − > 16. ____________________

17. ( )4 2 13x x+ < − 17. ____________________

18. 3 2 15 9x≤ − < 18. ____________________

19. 2

6 33

x +− < ≤ 19. ____________________

20. 3 9 and 4 4x x≤ − − ≥ − 20. ____________________

21. ( )6 3 2 6 or 7 3 2 3x x x− − > − < − + 21. ____________________

Solve.

22. Carlos drove 145 miles from 2 p.m. to 5:30 p.m. 22. ____________________ Find his average speed, rounded to the nearest mile per hour. 23. Jean can rent a car for a flat fee of $30 or for 23. ____________________

$18 plus 40 cents per mile. Use an inequality to describe the number of miles driven at which it is more economical to pay the flat fee.

24. Find three consecutive odd integers whose sum is 24. ____________________ equal to five more than two times the second largest number among the three numbers. 25. Find 25% of 4728. 25. ____________________



T- 21

Chapter 2 Test Form B


1. 2 6 4 8x x− = − 1. ____________________

2. ( ) ( )3 5 6 4 3 5 3 2x x x+ = + + − 2. ____________________

3. ( ) ( )5 3 4 4x x− = − 3. ____________________

4. ( ) ( )11 5 3 2 3 6x x x− − = − + + 4. _____________________

5. 3 22 3

x x− = − 5. ____________________

6. ( )2 13 1 4 3

4 3 12

xx x−− −+ = 6. ____________________

7. ( )3 2 2 5x x x− − = + 7. ____________________

8. 4 11

13

x += 8. ____________________

9. 7 4 4 11x − − = − 9. ____________________

10. ( )7 1 3 3 2 2n n n+ = − + 10. ____________________

11. ( ) ( )4 1 2 3x x− = − − 11. ____________________

Find the solution for each inequality. Write the answer in interval notation.

12. ( )8 5 11 1x x x− − > + 12. ____________________

13. ( )7 9 3x x− < − − ≤ − 13. ____________________

14. 2 7

13

x −> 14. ____________________



T- 22

Chapter 2 Test Form B cont’d

15. ( ) ( )5 2 2x x− ≥ − − 15. ____________________

16. 7 19

5 2 5

x− < − 16. ____________________

17. 5 2 8x− > 17. ____________________

18. ( ) ( )2 3 3 4x x− < + 18. ____________________

19. 2 6 11 21x≤ − < 19. ____________________

20. ( )2 3 4 or 4 6 6x x− < − < − 20. ____________________

21. 7 8 17 and 2 5 1x x− ≤ + > − 21. ____________________

Solve.

22. Find 15% of 740. 22. ____________________ 23. The sum of two consecutive odd integers is 76. 23. ____________________

Find the two integers.

24. In 2007, a high school had 9750 students. In 24. ____________________ 2008, they had an 8% increase in students. How students did they have in 2008?

25. Solve 2AC BC

A BB

+= + for C 25. ____________________



T- 23

Chapter 2 Test Form C


1. ( ) ( )7 3 2 14 6 2x x− = − − 1. ____________________

2. ( ) ( )3 2 5 2 6x x+ − = + 2. ____________________

3. ( )3 2 5 6 15x x− = − 3. ____________________

4. 4 3 5

4 6 3

x x x− + −+ = 4. _____________________

5. ( ) ( )3 2 4 6 5 1 11x x x x− + + = − + + 5. ____________________

6. 3 6 5 7x + − = 6. ____________________

7. 5 7 12 8x − + = 7. ____________________

8. 3 2

35

x−= 8. ____________________

9. 5 2 8x x+ = − 9. ____________________

10. ( )4 2 2 1 2x x+ = − − 10. ____________________

Solve each equation for the specified variable.

11. 7 9 3x y− = for y 11. ____________________

12. AB

AC D

=−

for D 12. ____________________

Solve each inequality. Write the answer in interval notation.

13. ( ) ( ) ( )8 1 3 1 5 3 2 9x x x− − + − < − + − 13. ____________________

14. ( ) ( )2 5 3 5x x− ≤ + 14. ____________________



T- 24

Chapter 2 Test Form C cont’d

15. ( )12 3 2 5 6x− ≤ − < 15. ____________________

16. ( )3 2 1

5 44

x −+ ≤ 16. ____________________

17. 1

22 3x

≥−

17. ____________________

18. ( )2 1 1

23 6

xx

−> − 18. ____________________

19. 2 6

2 04

x − − ≤

19. ____________________

20. 3 2 1x+ ≥ 20. ____________________

21. 2 4 and 4 9 3 6x x x− > + ≥ + 21. ____________________

Solve.

22. Find 18% of 1200. 22. ____________________ 23. A company finds that the cost C to make x items. 23. ____________________

monthly is given by 1197 23.2C x= + , and the monthly revenue R is given by the 27.19R x= . Use an inequality to find the minimum number of items that must be made and sold to make a profit.

24. Tamara has scores of 92, 74, 81, and 88 on her 24. ____________________ past exams. Find the minimum score she can make on the final exam to pass the course with an average of 70 or higher, given that the final exam counts as two tests. 25. Anne buys a house and pays $18,000 for a 25. ____________________ down payment. The down payment is 18% of the actual cost of the house. What is the actual cost of the house?



T- 25

Chapter 2 Test Form D

Circle the correct answer. Solve each equation.

1. ( )14 24 8 2 3 4x x− = − −

a. 0 b. 12 c. 2 d. 6

5

2. ( ) ( )5 2 3 1x x x− + = −

a. 5

7 b.

1

7 c. 1− d. 1

3. ( )0.6 4 1.2y + = −

a. −2 b. −6 c. −5.4 d. 2

4. ( ) ( )3 2 2 5 2 3 6 8x x− + = − +

a. −4 b. −3 c. Ø d. all real numbers

5. 4 5

52 3

x x+ −= +

a. −3 b. 5

6 c. 8 d. 12

6. 2 5 3 1

2 6

x x+ −=

a. 7−3 b. 16

3− c. 7

5

2 d.

8

3−

7. 3 6x − =

a. 9 b. −9 c. −3, 9 d. −9, 9



T- 26

Chapter 2 Test Form D cont’d

8. 5 7 4 1x − − = −

a. Ø b. 4

, 25

c. 4

2,5

− − d. 12

2,5

9. 2 3 1x x= −

a. 1

1,5

− b. −1, 1 c. 1

,15

d. 1

10. ( )4 1 8 4x x− = −

a. 3

0,2

b. Ø c. 3

2 d.

3 3,

2 2−

Solve each equation for the specified variable.

11. ( )2A B C D= − for D

a. 2C B

DB

−= b.

2BC AD

B

−= c.

2A BD

C

−= d.

2BC AD

B

−=

12. 32 3

A B BA

−+ = for A

a. 2

5

BA = − b.

5

3

BA = − c.

15

BA = − d.

5

BA = −

Solve each inequality.

13. ( ) ( )2 4 3 5 1 2x x− + ≥ + −

a. ( ,3)−∞ b. ( ,3]−∞ c.[ 3,3]− d. 8

,3

−∞ −

14. ( ) ( )3 2 3 5 1 1x x− + ≤ + −

a. ( ,5)−∞ b. 5

,8

∞

c. 5

,2

∞

d.

5,

8

−∞ −



T- 27


15. ( )5 3 7 4 3x x x− + ≥ −

a. ( ), 2−∞ b. 3

,2

−∞

c. ( , 2]−∞ − d. 2

,3

−∞ −

16. 7 2 3 5x− < + <

a. (−5, 1) b. (−2, 4) c. ( ) ( ), 5 1,−∞ − ∪ ∞ d. [ ]5,1−

17. 4 1

1 53

x −− ≤ <

a. [ )2,8− b. [ ]1, 4− c. 1

,42

−

d. (1, 4)

18. 3 or 1x x< ≥ − a. (−1, 3) b. [−1, 4] c. (−∞, ∞) d. Ø

19. 4 5 13x + <

a. 9

2,2

−

b. (−∞, 2) c. 9

, 22

− −

d. 9

,22

−

20. 2 3 27x − >

a. (−∞, 12) b. (−15, 12) c. (12, ∞) d. (−∞, −12) ∪ (15, ∞)

21. 4 9 1x + ≤

a. Ø b. all real numbers c. (−∞, −8] d. [−8, ∞)



T- 28


Solve.

22. Find 28% of 7450. a. 208,600 b. 2086 c. 266 d. 16,607

23. One number is 13 more than 5 times another. Their difference is 61. Find the two

numbers.

a. 42, 103 b. 20, 113 c. 12, 73 d. 141, 202

24. Ceiling tiles measuring 1 foot by 2 feet come 6 to a package. How many packages do you need to try to cover a rectangular ceiling that measures 12 feet by 18 feet?

a. 18 b. 216 c. 108 d. 9

25. A company finds that the cost, C, to produce x items is 560 12C x= + , while the revenue is 20.7R x= . Find the number of items to produce that will make the company break even.

a. 56 items b. 65 items c. 112 items d. 78 items



T- 29

Chapter 2 Test Form E


1. ( ) ( )2 4 1 3 5y y+ = − +

a. 17

11− b.

11

5− c.

19

11− d.

13

11−

2. ( ) ( )4 3 3 2 3 7 1y y y y+ − = − − +

a. −5 b. −3 c. Ø d. 6

3. ( )2 3 4 3 6x x x− + − = −

a. −12 b. 12 c. all real numbers d. Ø

4. 3 2

52

xx

+= −

a. −2 b. −12 c. 6 d. 9

2

5. ( )2 1 3 2

12 4 6

m m m+ −− =

a. −3 b. 7

9 c. 7 d.

7

9−

6. 3 4

36

x +=

a. 17 9

,3 3

− b. 7

3,3

− c. 14

9,3

− d. 22 14

,3 3

−

7. 3 8 6x + + =

a. −2 b. −2, 2 c. all real numbers d. Ø



T- 30

Chapter 1 Test Form E cont’d

8. 7 4 2 11x− + =

a. −4, 2 b. 2, 4 c. 1

,42

− d. 1

4,2

− −

9. 24 12 20 8x x+ = −

a. 1

,324

− b. 1

1,4

− c. 1

,14

− d. 1

2,4

−

Solve for the specified variable.

10. 1 2

2

r rR

+= for

2r

a. 2 1

2r R r= − b. 2 1

4 2r R= − c. 2 1

2r r R= − d. − 1

22

r Rr

+=

11. 3 11 4x y− = for y

a. 3 4

11

xy

−= b.

4 3

11

xy

−= c.

11 4

3

xy

−= d.

3 11

4

xy

−=

12. AB CB D+ = for B

a. B D A= − b. D

BA C

=+

c. D

BA C

=−

d. B A C D= + +


13. ( ) ( )2 4 1 3 2x x x− < + −

a. (−∞, 8) b. 4

,3

−∞

c. (−∞, −3) d. (−4, ∞)

14. ( )2 3 4 3 6x x− + < +

a. (−∞, −8) b. (−∞, 8) c. (−8, ∞) d. (8, ∞)



T- 31


15. ( )4 8 2 1

3 24 3

x xx x

+ +− < + −

a. (−∞, 8) b. (−∞, −4] c. [−2, ∞) d. (−∞, −2]

16. 3 6 3 9x− ≤ − <

a. [−1, 1) b. [−1, 2) c. [0, 2) d. (−∞, 0] ∪ (2, ∞)

17. 2 7

1 73

x −− < <

a. (−2, 14) b. (−5, 7) c. (−10, 14) d. (2, 14)

18. ( ) ( )7 1 14 and 3 5x x− + > − − <

a. (−∞, −3) ∪ (8, ∞) b. (−3, 8) c. (3, ∞) d. (8, ∞)

19. 4 12 2x + >

a. (−∞, −3] ∪ (8, ∞) b. 7 5

, ,2 2

−∞ − ∪ − ∞

c. 5 7

,2 2

−

d. 7 5

,2 2

− −

20. 7 6 2x + ≤ −

a. 8 4

,7 7

− −

b. 8 4

, ,7 7

−∞ − ∪ − ∞

c. { } d. 8 4

, ,7 7

−∞ − ∪ ∞



T- 32


21. 3 1

37

x −≤

a. 20 22

,3 3

−

b. 22 20

,3 3

− −

c. 22 20

,3 3

−

d. 20 22

, ,3 3

−∞ − ∪ ∞

Solve. 22. Find 17% of 476.

a. 2800 b. 28 c. 8092 d. 80.92 23. Find three consecutive integers such that the sum of the first two is the same as

sixteen more than the third.

a. −9, −8, −7 b. 17, 18, 19 c. 18, 19, 20 d. 23, 24, 25

24. Find the amount of money in an account after 12 years if a principal of $1800 was invested at 4.4% interest compounded quarterly. (Round to the nearest cent.)

a. $3049.02 b. $3212.25 c. $2971.77 d. $3043.18

25. Four times the sum of a number and six is the same as the difference of ten and three

times the number. Find the number.

a. −6 b. −2 c. 3 d. 1



T- 33

Chapter 2 Test Form F


1. ( ) ( ) ( )4 2 3 4 3 2x x x− − = − + − +

a. 2

19− b. −1 c.

5

7 d. 1

2. ( ) ( )3 5 8 4 5 2 7x x x− + − = −

a. 4 b. 2 c. −4 d. 0

3. 2 5 4 3

3 8

x x+ −=

a. 27

8− b.

31

4− c.

49

4− d.

49

28−

4. 2 4 3

6 2 3

m m m− + −− =

a. 5

2 b. 3 c. 1 d. −2

5. ( )6 5 5 3 1 2 4m m m− = − + − +

a. Ø b. 5

6 c. 0 d. all real numbers

6. 3 8x − =

a. 11 b. −11, 11 c. −5, 11 d. −5, 5

7. 5 3

53

x−=

a. 20 10

,3 3

− b. 10 20

,3 3

− c. 0, 10 d. −10, 0



T- 34

Chapter 2 Test Form F cont’d

8. 5 7 10 2x − + =

a. −1, 3 b. 1

,35

− c. Ø d. −3, 2

9. 2 1 3x x− = +

a. 2

,43

− b. 3

, 42

c. 4 d. 2

4,3

− −

Solve for the specified variable.

10. 5 11 6x y+ = for y

a. 5 6

11

xy

+= b.

11 5

6

xy

−= c.

6 5

11

xy

−= d.

11 6

5

xy

−=

11. 4 3 1

x y z+ = for y

a. 4

3

xzy

z x=

− b.

3

4

xzy

z x=

− c.

3

4

xzy

x z=

− d.

3

4

xzy

x z=

−

12. AC AD A+ = for C

a. C A D= − b. D

CA

= c. 1C D= − d. D

CA

= −


13. ( ) ( )2 7 3 5 2 3x x x− ≥ + −

a. 5

,7

∞

b. 11

,7

−∞

c. 12

,7

∞

d. 23

,13

∞

14. 3 24

x− <

a. (4, ∞) b. (−∞, 4) c. [4, ∞) d. (-∞, 4]



T- 35


15. ( )8 4 2 6 12x− < + <

a. 3

3,2

−

b. 3

4,2

− −

c. 1

,42

−

d. (−3, −2)

16. 3 4

5 13

x +− ≤ ≤ −

a. 19 7

,3 3

− −

b. 11 4

,3 3

− −

c. 11 1

,3 3

−

d. 5 1

,3 3

− −

17. 3 9 and 2 10 4x x x− > + ≥ +

a. (−∞, −6] ∪ (−3, ∞) b. (−∞, ∞) c. [−6, 3) d. [−6, −3)

18. 3

3 14

x − ≤

a. 5 1

,12 4

−

b. 1 1

,12 2

−

c. 1 7

,12 12

−

d. 1 7

,12 12

19. 5 8 3x − + =

a. 0 b. −10 c. −10, 0 d. Ø

20. 3 22

x− >

a. (−∞, −2) ∪ (4, ∞) b. (−∞, 2) ∪ (10, ∞) c. (2, 6) d. (−2, 10)

21. ( )4 3 2

4 27

x−+ ≤

a. 7

,32

−

b. 1 13

, ,4 4

−∞ − ∪ ∞

c. Ø d. (−∞, ∞)



T- 36


Solve. 22. Find 25% of 7200.

a. 1800 b. 288 c. 9000 d. 7488 23. Paul can rent equipment for $35 per day, or he can rent it at a cost of $20 plus $4 per

hour of use. Use an inequality to find the number of hours of use (to the nearest hour) at which it is more economical to pay the single fee for the day.

a. 5 hours b. 4 hours c. 2 hours d. 3 hours

24. A gallon of paint can cover 500 square feet. Find how many gallons (to the nearest gallon) should be purchased to paint two coats on each wall of a rectangular room whose dimensions are 22 feet by 24 feet with 8-foot ceilings.

a. 2 gallons b. 4 gallons c. 5 gallons d. 3 gallons

25. A furniture store is offering a 35% discount on the price of a discontinued sofa. If the discounted price of the sofa is $637, find the regular price.

a. $980 b. $414.05 c. $1820 d. $1095


testbanktop.comtestbanktop.com/wp-content/uploads/2016/12/downloadable-solution... · m-6...

Documents