Content check — Prealgebra, Chapter 8: Solving Linear Equations

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 8: Solving Linear Equations

272 problems · 0 figures

Be Prepared 8.1 §8.1 source ↗

Solve:

n - 12 = 16 .

If you missed this problem, review Example 2.33.

Example 2.33 in the book ↗

Answer

28

Be Prepared 8.2 §8.1 source ↗

Translate into algebra ‘five less than

x .’

If you missed this problem, review Example 2.24.

Example 2.24 in the book ↗

Answer

x - 5

Be Prepared 8.3 §8.1 source ↗

x = 2

a solution to

5 x - 3 = 7 ?

If you missed this problem, review Example 2.28.

Example 2.28 in the book ↗

Answer

yes

Try It 8.1 §8.1 source ↗

y = \frac{2}{3}

a solution for

9 y + 2 = 6 y ?

Answer

Try It 8.2 §8.1 source ↗

y = \frac{2}{5}

a solution for

5 y - 3 = 10 y ?

Answer

Try It 8.3 §8.1 source ↗

Solve:

x + 9 = −7 .

Answer

x = −16

Try It 8.4 §8.1 source ↗

Solve:

x + 16 = −4 .

Answer

x = −20

Try It 8.5 §8.1 source ↗

Solve:

n - 6 = −7 .

Answer

n = −1

Try It 8.6 §8.1 source ↗

Solve:

x - 5 = −9 .

Answer

x = −4

Try It 8.7 §8.1 source ↗

Solve:

p - \frac{1}{3} = \frac{5}{6} .

Answer

p = \frac{7}{6}

Try It 8.8 §8.1 source ↗

Solve:

q - \frac{1}{2} = \frac{1}{6} .

Answer

q = \frac{2}{3}

Try It 8.9 §8.1 source ↗

Solve:

b - 2.8 = 3.6 .

Answer

b = 6.4

Try It 8.10 §8.1 source ↗

Solve:

c - 6.9 = 7.1 .

Answer

c = 14

Try It 8.11 §8.1 source ↗

Solve:

8 y -

4 -

7 y -

7 =

4 .

Answer

y = 15

Try It 8.12 §8.1 source ↗

Solve:

6 z +

5 -

5 z -

4 =

3 .

Answer

z = 2

Try It 8.13 §8.1 source ↗

Solve:

5 (p - 3) -

4 p =

−10 .

Answer

p = 5

Try It 8.14 §8.1 source ↗

Solve:

4 (q + 2) -

3 q =

−8 .

Answer

q = −16

Try It 8.15 §8.1 source ↗

Solve:

4 (2 h - 3) -

7 h =

−6 -

7 .

Answer

h = −1

Try It 8.16 §8.1 source ↗

Solve:

2 (5 x + 2) -

9 x =

−2 +

7 .

Answer

x = 1

Try It 8.17 §8.1 source ↗

Translate and solve: Eleven more than

x

is equal to

41 .

Answer

x + 11 = 41; x = 30

Try It 8.18 §8.1 source ↗

Translate and solve: Twelve less than

y

is equal to

51 .

Answer

y − 12 = 51; y = 63

Try It 8.19 §8.1 source ↗

Translate and solve: The difference of

4 x

and

3 x

14 .

Answer

4x − 3x = 14; x = 14

Try It 8.20 §8.1 source ↗

Translate and solve: The difference of

7 a

and

6 a

−8 .

Answer

7a − 6a = −8; a = −8

Try It 8.21 §8.1 source ↗

Translate into an algebraic equation and solve: The Pappas family has two cats, Zeus and Athena. Together, they weigh

13

pounds. Zeus weighs

6

pounds. How much does Athena weigh?

Answer

a + 6 = 13; Athena weighs 7 pounds.

Try It 8.22 §8.1 source ↗

Translate into an algebraic equation and solve: Sam and Henry are roommates. Together, they have

68

books. Sam has

26

books. How many books does Henry have?

Answer

26 + h = 68; Henry has 42 books.

Try It 8.23 §8.1 source ↗

Translate into an algebraic equation and solve: Eddie paid

$19,875

for his new car. This was

$1,025

less than the sticker price. What was the sticker price of the car?

Answer

19,875 = s − 1025; the sticker price is $20,900.

Try It 8.24 §8.1 source ↗

Translate into an algebraic equation and solve: The admission price for the movies during the day is

$7.75 .

This is

$3.25

less than the price at night. How much does the movie cost at night?

Answer

7.75 = n − 3.25; the price at night is $11.00.

8.1-1 §8.1 source ↗

Solve Equations Using the Subtraction and Addition Properties of Equality

In the following exercises, determine whether the given value is a solution to the equation.

Is $y = \frac{1}{3}$ a solution of $4 y + 2 = 10 y ?$

Answer

yes

8.1-3 §8.1 source ↗

Solve Equations Using the Subtraction and Addition Properties of Equality

In the following exercises, determine whether the given value is a solution to the equation.

Is $u = − \frac{1}{2}$ a solution of $8 u - 1 = 6 u ?$

Answer

8.1-5 §8.1 source ↗

In the following exercises, solve each equation.

$x + 7 = 12$

Answer

x = 5

8.1-7 §8.1 source ↗

In the following exercises, solve each equation.

$b + \frac{1}{4} = \frac{3}{4}$

Answer

b = \frac{1}{2}

8.1-9 §8.1 source ↗

In the following exercises, solve each equation.

$p + 2.4 = −9.3$

Answer

p = −11.7

8.1-11 §8.1 source ↗

In the following exercises, solve each equation.

$a - 3 = 7$

Answer

a = 10

8.1-13 §8.1 source ↗

In the following exercises, solve each equation.

$x - \frac{1}{3} = 2$

Answer

x = \frac{7}{3}

8.1-15 §8.1 source ↗

In the following exercises, solve each equation.

$y - 3.8 = 10$

Answer

y = 13.8

8.1-17 §8.1 source ↗

In the following exercises, solve each equation.

$x - 15 = −42$

Answer

x = −27

8.1-19 §8.1 source ↗

In the following exercises, solve each equation.

$q + \frac{3}{4} = \frac{1}{2}$

Answer

q = - \frac{1}{4}

8.1-21 §8.1 source ↗

In the following exercises, solve each equation.

$y - \frac{3}{4} = \frac{3}{5}$

Answer

y = \frac{27}{20}

8.1-23 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$m + 6 - 8 = 15$

Answer

m = 17

8.1-25 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$6 x +$ $8 -$ $5 x +$ $16 =$ $32$

Answer

x = 8

8.1-27 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$−8 n -$ $17 +$ $9 n -$ $4 =$ $−41$

Answer

n = −20

8.1-29 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$4 (y - 2) -$ $3 y =$ $−6$

Answer

y = 2

8.1-31 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$5 (w + 2.2) -$ $4 w =$ $9.3$

Answer

w = −1.7

8.1-33 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$−8 (x - 1) +$ $9 x =$ $−3 +$ $9$

Answer

x = −2

8.1-35 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$2 (8 m + 3) -$ $15 m -$ $4 =$ $3 -$ $5$

Answer

m = −4

8.1-37 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$-$ $(k + 7) +$ $2 k +$ $8 =$ $7$

Answer

k = 6

8.1-39 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$8 c -$ $7 (c - 3) +$ $4 =$ $−16$

Answer

c = −41

8.1-41 §8.1 source ↗

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

$6 (9 y - 1) -$ $10 (5 y) -$ $3 y =$ $22$

Answer

y = 28

8.1-43 §8.1 source ↗

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

The sum of $x$ and $−5$ is $33 .$

Answer

x + (−5) = 33; x = 38

8.1-45 §8.1 source ↗

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

Three less than $y$ is $−19 .$

Answer

y − 3 = −19; y = −16

8.1-47 §8.1 source ↗

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

Eight more than $p$ is equal to $52 .$

Answer

p + 8 = 52; p = 44

8.1-49 §8.1 source ↗

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

The difference of $5 c$ and $4 c$ is $60 .$

Answer

5c − 4c = 60; c = 60

8.1-51 §8.1 source ↗

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

The difference of $f$ and $\frac{1}{3}$ is $\frac{1}{12} .$

Answer

f -

\frac{1}{3} =

\frac{1}{12};

f =

\frac{5}{12}

8.1-53 §8.1 source ↗

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

The sum of $−9 m$ and $10 m$ is $−25 .$

Answer

−9m + 10m = −25; m = −25

8.1-55 §8.1 source ↗

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Jeff read a total of $54$ pages in his English and Psychology textbooks. He read $41$ pages in his English textbook. How many pages did he read in his Psychology textbook?

Answer

Let p equal the number of pages read in the Psychology book. 41 + p = 54. Jeff read 13 pages in his Psychology book.

8.1-57 §8.1 source ↗

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Eva’s daughter is $5$ years younger than her son. Eva’s son is $12$ years old. How old is her daughter?

Answer

Let d equal the daughter’s age. d = 12 − 5. Eva’s daughter’s age is 7 years old.

8.1-59 §8.1 source ↗

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

For a family birthday dinner, Celeste bought a turkey that weighed $5$ pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed $16$ pounds. How much did the Thanksgiving turkey weigh?

Answer

21 pounds

8.1-61 §8.1 source ↗

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Connor’s temperature was $0.7$ degrees higher this morning than it had been last night. His temperature this morning was $101.2$ degrees. What was his temperature last night?

Answer

100.5 degrees

8.1-63 §8.1 source ↗

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Ron’s paycheck this week was $$17.43$ less than his paycheck last week. His paycheck this week was $$103.76 .$ How much was Ron’s paycheck last week?

Answer

$121.19

8.1-65 §8.1 source ↗

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Construction Miguel wants to drill a hole for a $\frac{5}{8} -inch$ screw. The screw should be $\frac{1}{12}$ inch larger than the hole. Let $d$ equal the size of the hole he should drill. Solve the equation $d + \frac{1}{12} = \frac{5}{8}$ to see what size the hole should be.

Answer

d = \frac{13}{24}

8.1-67 §8.1 source ↗

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Write a word sentence that translates the equation $y - 18 = 41$ and then make up an application that uses this equation in its solution.

Answer

Answers will vary.

Be Prepared 8.4 §8.2 source ↗

Simplify:

−7 (\frac{1}{−7}) .

If you missed this problem, review Example 4.28.

Example 4.28 in the book ↗

Answer

1

Be Prepared 8.5 §8.2 source ↗

What is the reciprocal of

- \frac{3}{8} ?

If you missed this problem, review Example 4.29.

Example 4.29 in the book ↗

Answer

- \frac{8}{3}

Be Prepared 8.6 §8.2 source ↗

Evaluate

9 x + 2

when

x = −3 .

If you missed this problem, review Example 3.56.

Example 3.56 in the book ↗

Answer

- 25

Try It 8.25 §8.2 source ↗

Solve:

3 y = −48 .

Answer

y = −16

Try It 8.26 §8.2 source ↗

Solve:

4 z = −52 .

Answer

z = −13

Try It 8.27 §8.2 source ↗

Solve:

\frac{b}{−6} = −24 .

Answer

b = 144

Try It 8.28 §8.2 source ↗

Solve:

\frac{c}{−8} = −16 .

Answer

c = 128

Try It 8.29 §8.2 source ↗

Solve:

- k = 8 .

Answer

k = −8

Try It 8.30 §8.2 source ↗

Solve:

- g = 3 .

Answer

g = −3

Try It 8.31 §8.2 source ↗

Solve:

\frac{2}{5} n = 14 .

Answer

n = 35

Try It 8.32 §8.2 source ↗

Solve:

\frac{5}{6} y = 15 .

Answer

y = 18

Try It 8.33 §8.2 source ↗

Solve:

7 x +

6 x -

4 x =

−8 +

26 .

Answer

x = 2

Try It 8.34 §8.2 source ↗

Solve:

11 n -

3 n -

6 n =

7 -

17 .

Answer

n = −5

Try It 8.35 §8.2 source ↗

Solve:

18 -

27 =

15 c -

9 c -

3 c .

Answer

c = −3

Try It 8.36 §8.2 source ↗

Solve:

18 -

22 =

12 x -

x -

4 x .

Answer

x = - \frac{4}{7}

Try It 8.37 §8.2 source ↗

Solve:

−4 (n - 2) -

8 =

24 .

Answer

n = −6

Try It 8.38 §8.2 source ↗

Solve:

−6 (n - 2) -

12 =

30 .

Answer

n = −5

8.2-69 §8.2 source ↗

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.

$7 p = 63$

Answer

p = 9

8.2-71 §8.2 source ↗

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.

$−9 x = −27$

Answer

x = 3

8.2-73 §8.2 source ↗

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.

$−72 = 12 y$

Answer

y = −6

8.2-75 §8.2 source ↗

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.

$−8 m = −56$

Answer

m = 7

8.2-77 §8.2 source ↗

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.

$0.75 a = 11.25$

Answer

a = 15

8.2-79 §8.2 source ↗

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.

$4 x = 0$

Answer

x = 0

8.2-81 §8.2 source ↗

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$\frac{z}{2} = 14$

Answer

z = 28

8.2-83 §8.2 source ↗

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$\frac{c}{−3} = −12$

Answer

c = 36

8.2-85 §8.2 source ↗

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$\frac{q}{6} = −8$

Answer

q = −48

8.2-87 §8.2 source ↗

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$−4 = \frac{p}{−20}$

Answer

p = 80

8.2-89 §8.2 source ↗

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$\frac{3}{5} r = 15$

Answer

r = 25

8.2-91 §8.2 source ↗

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$24 = - \frac{3}{4} x$

Answer

x = −32

8.2-93 §8.2 source ↗

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.

$- \frac{1}{3} q = - \frac{5}{6}$

Answer

q = \frac{5}{2}

8.2-95 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

$6 y -$ $3 y +$ $12 y =$ $−43 +$ $28$

Answer

y = −1

8.2-97 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

$−5 m +$ $7 m -$ $8 m =$ $−6 +$ $36$

Answer

m = −5

8.2-99 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

$−18 -$ $7 =$ $5 t -$ $9 t -$ $6 t$

Answer

t = \frac{5}{2}

8.2-101 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

$\frac{5}{12} q +$ $\frac{1}{2} q =$ $25 -$ $3$

Answer

q = 24

8.2-103 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

$0.05 p -$ $0.01 p =$ $2 +$ $0.24$

Answer

p = 56

8.2-105 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

Teaching Connie’s kindergarten class has $24$ children. She wants them to get into $4$ equal groups. Find the number of children in each group, $g,$ by solving the equation $4 g = 24 .$

Answer

6 children

8.2-107 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

Unit price Nishant paid $$12.96$ for a pack of $12$ juice bottles. Find the price of each bottle, $b,$ by solving the equation $12 b = 12.96 .$

Answer

$1.08

8.2-109 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

Fabric The drill team used $14$ yards of fabric to make flags for one-third of the members. Find how much fabric, $f,$ they would need to make flags for the whole team by solving the equation $\frac{1}{3} f = 14 .$

Answer

42 yards

8.2-111 §8.2 source ↗

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

Emiliano thinks $x = 40$ is the solution to the equation $\frac{1}{2} x = 80 .$ Explain why he is wrong.

Answer

Answer will vary.

Be Prepared 8.7 §8.3 source ↗

Simplify:

4 y - 9 + 9 .

If you missed this problem, review Example 2.22.

Example 2.22 in the book ↗

Answer

4 y

Be Prepared 8.8 §8.3 source ↗

Solve:

y + 12 = 16 .

If you missed this problem, review Example 2.31.

Example 2.31 in the book ↗

Answer

4

Be Prepared 8.9 §8.3 source ↗

Solve:

−3 y = 63 .

If you missed this problem, review Example 3.65.

Example 3.65 in the book ↗

Answer

- 21

Try It 8.39 §8.3 source ↗

Solve:

3 x + 4 = −8 .

Answer

x = −4

Try It 8.40 §8.3 source ↗

Solve:

5 a + 3 = −37 .

Answer

a = −8

Try It 8.41 §8.3 source ↗

Solve:

5 y - 9 = 16 .

Answer

y = 5

Try It 8.42 §8.3 source ↗

Solve:

3 m - 8 = 19 .

Answer

m = 9

Try It 8.43 §8.3 source ↗

Solve:

6 n = 5 n + 10 .

Answer

n = 10

Try It 8.44 §8.3 source ↗

Solve:

−6 c = −7 c + 1 .

Answer

c = 1

Try It 8.45 §8.3 source ↗

Solve:

3 p - 14 = 5 p .

Answer

p = −7

Try It 8.46 §8.3 source ↗

Solve:

8 m + 9 = 5 m .

Answer

m = −3

Try It 8.47 §8.3 source ↗

Solve:

12 j = −4 j + 32 .

Answer

j = 2

Try It 8.48 §8.3 source ↗

Solve:

8 h = −4 h + 12 .

Answer

h = 1

Try It 8.49 §8.3 source ↗

Solve:

12 x + 8 = 6 x + 2 .

Answer

x = −1

Try It 8.50 §8.3 source ↗

Solve:

9 y + 4 = 7 y + 12 .

Answer

y = 4

Try It 8.51 §8.3 source ↗

Solve:

8 q - 5 = −4 q + 7 .

Answer

q = 1

Try It 8.52 §8.3 source ↗

Solve:

7 n - 3 = n + 3 .

Answer

n = 1

Try It 8.53 §8.3 source ↗

Solve:

2 a - 2 = 6 a + 18 .

Answer

a = −5

Try It 8.54 §8.3 source ↗

Solve:

4 k - 1 = 7 k + 17 .

Answer

k = −6

Try It 8.55 §8.3 source ↗

Solve:

\frac{7}{8} x -

12 =

-

\frac{1}{8} x -

2 .

Answer

x = 10

Try It 8.56 §8.3 source ↗

Solve:

\frac{7}{6} y +

11 =

\frac{1}{6} y +

8 .

Answer

y = −3

Try It 8.57 §8.3 source ↗

Solve:

2.8 x +

12 =

−1.4 x -

9 .

Answer

x = −5

Try It 8.58 §8.3 source ↗

Solve:

3.6 y +

8 =

1.2 y -

4 .

Answer

y = −5

Try It 8.59 §8.3 source ↗

Solve:

5 (x + 3) = 35 .

Answer

x = 4

Try It 8.60 §8.3 source ↗

Solve:

6 (y - 4) = −18 .

Answer

y = 1

Try It 8.61 §8.3 source ↗

Solve:

- (y + 8) = −2 .

Answer

y = −6

Try It 8.62 §8.3 source ↗

Solve:

- (z + 4) = −12 .

Answer

z = 8

Try It 8.63 §8.3 source ↗

Solve:

2 (a - 4) +

3 =

−1 .

Answer

a = 2

Try It 8.64 §8.3 source ↗

Solve:

7 (n - 3) -

8 =

−15 .

Answer

n = 2

Try It 8.65 §8.3 source ↗

Solve:

12 -

3 (4 j + 3) =

−17 .

Answer

j = \frac{5}{3}

Try It 8.66 §8.3 source ↗

Solve:

−6 -

8 (k - 2) =

−10 .

Answer

k = \frac{5}{2}

Try It 8.67 §8.3 source ↗

Solve:

6 (p - 3) -

7 =

5 (4 p + 3) -

12 .

Answer

p = −2

Try It 8.68 §8.3 source ↗

Solve:

8 (q + 1) -

5 =

3 (2 q - 4) -

1 .

Answer

q = −8

Try It 8.69 §8.3 source ↗

Solve:

\frac{1}{3} (6 u + 3) =

7 -

u .

Answer

u = 2

Try It 8.70 §8.3 source ↗

Solve:

\frac{2}{3} (9 x - 12) =

8 +

2 x .

Answer

x = 4

Try It 8.71 §8.3 source ↗

Solve:

0.55 (100 n + 8) =

0.6 (85 n + 14) .

Answer

n = 1

Try It 8.72 §8.3 source ↗

Solve:

0.15 (40 m - 120) =

0.5 (60 m + 12) .

Answer

m = −1

8.3-113 §8.3 source ↗

Solve an Equation with Constants on Both Sides

In the following exercises, solve the equation for the variable.

$7 x - 8 = 34$

Answer

x = 6

8.3-115 §8.3 source ↗

Solve an Equation with Constants on Both Sides

In the following exercises, solve the equation for the variable.

$14 y + 7 = 91$

Answer

y = 6

8.3-117 §8.3 source ↗

Solve an Equation with Constants on Both Sides

In the following exercises, solve the equation for the variable.

$4 m + 9 = −23$

Answer

m = −8

8.3-119 §8.3 source ↗

Solve an Equation with Constants on Both Sides

In the following exercises, solve the equation for the variable.

$−47 = 6 b + 1$

Answer

b = −8

8.3-121 §8.3 source ↗

Solve an Equation with Constants on Both Sides

In the following exercises, solve the equation for the variable.

$29 = −8 x - 3$

Answer

x = −4

8.3-123 §8.3 source ↗

Solve an Equation with Constants on Both Sides

In the following exercises, solve the equation for the variable.

$−14 q - 15 = 13$

Answer

q = −2

8.3-125 §8.3 source ↗

Solve an Equation with Variables on Both Sides

In the following exercises, solve the equation for the variable.

$9 k = 8 k - 11$

Answer

k = −11

8.3-127 §8.3 source ↗

Solve an Equation with Variables on Both Sides

In the following exercises, solve the equation for the variable.

$6 x + 27 = 9 x$

Answer

x = 9

8.3-129 §8.3 source ↗

Solve an Equation with Variables on Both Sides

In the following exercises, solve the equation for the variable.

$b = −4 b - 15$

Answer

b = −3

8.3-131 §8.3 source ↗

Solve an Equation with Variables on Both Sides

In the following exercises, solve the equation for the variable.

$7 z = 39 - 6 z$

Answer

z = 3

8.3-133 §8.3 source ↗

Solve an Equation with Variables on Both Sides

In the following exercises, solve the equation for the variable.

$8 x + \frac{3}{4} = 7 x$

Answer

x = - \frac{3}{4}

8.3-135 §8.3 source ↗

Solve an Equation with Variables on Both Sides

In the following exercises, solve the equation for the variable.

$−15 r - 8 = −11 r$

Answer

r = −2

8.3-137 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$4 x - 17 = 3 x + 2$

Answer

x = 19

8.3-139 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$21 + 6 f = 7 f + 14$

Answer

f = 7

8.3-141 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$8 q - 5 = 5 q - 20$

Answer

q = −5

8.3-143 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$9 c + 7 = −2 c - 37$

Answer

c = −4

8.3-145 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$12 x -$ $17 =$ $−3 x +$ $13$

Answer

x = 2

8.3-147 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$3 y - 4 = 12 - y$

Answer

y = 4

8.3-149 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$\frac{4}{3} m -$ $7 =$ $\frac{1}{3} m -$ $13$

Answer

m = −6

8.3-151 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$11 -$ $\frac{1}{4} a =$ $\frac{3}{4} a +$ $4$

Answer

a = 7

8.3-153 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$\frac{5}{4} a +$ $15 =$ $\frac{3}{4} a -$ $5$

Answer

a = −40

8.3-155 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$\frac{3}{5} p + 2 = \frac{4}{5} p - 1$

Answer

p = 15

8.3-157 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$13 z +$ $6.45 =$ $8 z +$ $23.75$

Answer

z = 3.46

8.3-159 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$2.7 w -$ $80 =$ $1.2 w +$ $10$

Answer

w = 60

8.3-161 §8.3 source ↗

Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

$6.6 x -$ $18.9 =$ $3.4 x +$ $54.7$

Answer

x = 23

8.3-163 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$4 (y + 7) = 64$

Answer

y = 9

8.3-165 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$9 = 3 (x - 3)$

Answer

x = 6

8.3-167 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$14 (y - 6) = −42$

Answer

y = 3

8.3-169 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$−7 (3 n + 4) = 14$

Answer

n = −2

8.3-171 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$8 (3 + 3 p) = 0$

Answer

p = −1

8.3-173 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$\frac{3}{5} (10 x - 5) =$ $27$

Answer

x = 5

8.3-175 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$4 (2.5 v - 0.6) =$ $7.6$

Answer

v = 1

8.3-177 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$0.5 (16 m + 34) =$ $−15$

Answer

m = 0.25

8.3-179 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$- (t - 8) = 17$

Answer

t = −9

8.3-181 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$8 (6 b - 7) +$ $23 =$ $63$

Answer

b = 2

8.3-183 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$13 +$ $2 (m - 4) =$ $17$

Answer

m = 6

8.3-185 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$−9 +$ $6 (5 - k) =$ $12$

Answer

k = \frac{3}{2}

8.3-187 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$18 -$ $(9 r + 7) =$ $−16$

Answer

r = 3

8.3-189 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$18 -$ $2 (y - 3) =$ $32$

Answer

y = −4

8.3-191 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$3 (4 n - 1) -$ $2 =$ $8 n +$ $3$

Answer

n = 2

8.3-193 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$5 (x - 4) -$ $4 x =$ $14$

Answer

x = 34

8.3-195 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$5 +$ $6 (3 s - 5) =$ $−3 +$ $2 (8 s - 1)$

Answer

s = 10

8.3-197 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

$4 (x - 1) -$ $8 =$ $6 (3 x - 2) -$ $7$

Answer

x = \frac{1}{2}

8.3-199 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

Making a fence Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is $150$ feet. The length is $15$ feet more than the width. Find the width, $w,$ by solving the equation $150 =$ $2 (w + 15) +$ $2 w .$

Answer

30 feet

8.3-201 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

Coins Rhonda has $$1.90$ in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, $n,$ by solving the equation $0.05 n +$ $0.10 (2 n - 1) =$ $1.90 .$

Answer

8 nickels

8.3-203 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

When solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient as the variable side?

Answer

Answers will vary.

8.3-205 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

What is the first step you take when solving the equation $3 -$ $7 (y - 4) =$ $38 ?$ Explain why this is your first step.

Answer

Answers will vary.

8.3-207 §8.3 source ↗

Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

Using your own words, list the steps in the General Strategy for Solving Linear Equations.

Answer

Answers will vary.

Be Prepared 8.10 §8.4 source ↗

Multiply:

8 \cdot \frac{3}{8} .

If you missed this problem, review Example 4.28

Example 4.28 in the book ↗

Answer

3

Be Prepared 8.11 §8.4 source ↗

Find the LCD of

\frac{5}{6} and \frac{1}{4} .

If you missed this problem, review Example 4.63

Example 4.63 in the book ↗

Answer

12

Be Prepared 8.12 §8.4 source ↗

Multiply:

4.78

100 .

If you missed this problem, review Example 5.18

Example 5.18 in the book ↗

Answer

478

Try It 8.73 §8.4 source ↗

Solve:

\frac{1}{4} x + \frac{1}{2} = \frac{5}{8} .

Answer

x = \frac{1}{2}

Try It 8.74 §8.4 source ↗

Solve:

\frac{1}{6} y - \frac{1}{3} = \frac{1}{6} .

Answer

y = 3

Try It 8.75 §8.4 source ↗

Solve:

6 =

\frac{1}{2} v +

\frac{2}{5} v -

\frac{3}{4} v .

Answer

v = 40

Try It 8.76 §8.4 source ↗

Solve:

−1 =

\frac{1}{2} u +

\frac{1}{4} u -

\frac{2}{3} u .

Answer

u = −12

Try It 8.77 §8.4 source ↗

Solve:

a +

\frac{3}{4} =

\frac{3}{8} a -

\frac{1}{2} .

Answer

a = −2

Try It 8.78 §8.4 source ↗

Solve:

c +

\frac{3}{4} =

\frac{1}{2} c -

\frac{1}{4} .

Answer

c = −2

Try It 8.79 §8.4 source ↗

Solve:

−11 =

\frac{1}{2} (6 p + 2) .

Answer

p = −4

Try It 8.80 §8.4 source ↗

Solve:

8 = \frac{1}{3} (9 q + 6) .

Answer

q = 2

Try It 8.81 §8.4 source ↗

Solve:

\frac{1}{5} (n + 3) =

\frac{1}{4} (n + 2) .

Answer

n = 2

Try It 8.82 §8.4 source ↗

Solve:

\frac{1}{2} (m - 3) =

\frac{1}{4} (m - 7) .

Answer

m = −1

Try It 8.83 §8.4 source ↗

Solve:

0.6 x - 1 = 11 .

Answer

x = 20

Try It 8.84 §8.4 source ↗

Solve:

1.2 x - 3 = 9 .

Answer

x = 10

Try It 8.85 §8.4 source ↗

Solve:

0.14 h +

0.12 =

0.35 h -

2.4 .

Answer

h = 12

Try It 8.86 §8.4 source ↗

Solve:

0.65 k -

0.1 =

0.4 k -

0.35 .

Answer

k = −1

Try It 8.87 §8.4 source ↗

Solve:

0.25 n +

0.05 (n + 5) =

2.95 .

Answer

n = 9

Try It 8.88 §8.4 source ↗

Solve:

0.10 d +

0.05 (d - 5) =

2.15 .

Answer

d = 16

8.4-209 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{1}{4} x - \frac{1}{2} = - \frac{3}{4}$

Answer

x = −1

8.4-211 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{5}{6} y - \frac{2}{3} = - \frac{3}{2}$

Answer

y = −1

8.4-213 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{1}{2} a + \frac{3}{8} = \frac{3}{4}$

Answer

a = \frac{3}{4}

8.4-215 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$2 =$ $\frac{1}{3} x -$ $\frac{1}{2} x +$ $\frac{2}{3} x$

Answer

x = 4

8.4-217 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{1}{4} m -$ $\frac{4}{5} m +$ $\frac{1}{2} m =$ $−1$

Answer

m = 20

8.4-219 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$x + \frac{1}{2} = \frac{2}{3} x - \frac{1}{2}$

Answer

x = −3

8.4-221 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{1}{3} w + \frac{5}{4} = w - \frac{1}{4}$

Answer

w = \frac{9}{4}

8.4-223 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{1}{2} x -$ $\frac{1}{4} =$ $\frac{1}{12} x +$ $\frac{1}{6}$

Answer

x = 1

8.4-225 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{1}{3} b +$ $\frac{1}{5} =$ $\frac{2}{5} b -$ $\frac{3}{5}$

Answer

b = 12

8.4-227 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$1 = \frac{1}{6} (12 x - 6)$

Answer

x = 1

8.4-229 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{1}{4} (p - 7) =$ $\frac{1}{3} (p + 5)$

Answer

p = −41

8.4-231 §8.4 source ↗

Solve equations with fraction coefficients

In the following exercises, solve the equation by clearing the fractions.

$\frac{1}{2} (x + 4) = \frac{3}{4}$

Answer

x = - \frac{5}{2}

8.4-233 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

$0.6 y + 3 = 9$

Answer

y = 10

8.4-235 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

$3.6 j - 2 = 5.2$

Answer

j = 2

8.4-237 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

$0.4 x +$ $0.6 =$ $0.5 x -$ $1.2$

Answer

x = 18

8.4-239 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

$0.23 x +$ $1.47 =$ $0.37 x -$ $1.05$

Answer

x = 18

8.4-241 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

$0.9 x -$ $1.25 =$ $0.75 x +$ $1.75$

Answer

x = 20

8.4-243 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

$0.05 n +$ $0.10 (n + 8) =$ $2.15$

Answer

n = 9

8.4-245 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

$0.10 d +$ $0.25 (d + 5) =$ $4.05$

Answer

d = 8

8.4-247 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

$0.05 (q - 5) +$ $0.25 q =$ $3.05$

Answer

q = 11

8.4-249 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

Coins Taylor has $$2.00$ in dimes and pennies. The number of pennies is $2$ more than the number of dimes. Solve the equation $0.10 d +$ $0.01 (d + 2) =$ $2$ for $d,$ the number of dimes.

Answer

d = 18

8.4-251 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

Explain how to find the least common denominator of $\frac{3}{8},$ $\frac{1}{6},$ $and \frac{2}{3} .$

Answer

Answers will vary.

8.4-253 §8.4 source ↗

Solve Equations with Decimal Coefficients

In the following exercises, solve the equation by clearing the decimals.

If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?

Answer

Answers will vary.

8.R-255 §8.R source ↗

In the following exercises, determine whether the given number is a solution to the equation.

$x +$ $16 =$ $31,$ $x =$ $15$

Answer

yes

8.R-257 §8.R source ↗

In the following exercises, determine whether the given number is a solution to the equation.

$−9 n = 45, n = 54$

Answer

8.R-259 §8.R source ↗

In the following exercises, solve the equation using the Subtraction Property of Equality.

$x + 7 = 19$

Answer

8.R-261 §8.R source ↗

In the following exercises, solve the equation using the Subtraction Property of Equality.

$a + \frac{1}{3} = \frac{5}{3}$

Answer

a = \frac{4}{3}

8.R-263 §8.R source ↗

In the following exercises, solve the equation using the Addition Property of Equality.

$u - 7 = 10$

Answer

u = 17

8.R-265 §8.R source ↗

In the following exercises, solve the equation using the Addition Property of Equality.

$c - \frac{3}{11} = \frac{9}{11}$

Answer

c = \frac{12}{11}

8.R-267 §8.R source ↗

In the following exercises, solve the equation.

$n - 12 = 32$

Answer

n = 44

8.R-269 §8.R source ↗

In the following exercises, solve the equation.

$f + \frac{2}{3} = 4$

Answer

f = \frac{10}{3}

8.R-271 §8.R source ↗

In the following exercises, solve the equation.

$y + 8 - 15 = −3$

Answer

y = 4

8.R-273 §8.R source ↗

In the following exercises, solve the equation.

$6 (n - 1) -$ $5 n =$ $−14$

Answer

n = −8

8.R-275 §8.R source ↗

In the following exercises, translate each English sentence into an algebraic equation and then solve it.

The sum of $−6$ and $m$ is $25 .$

Answer

−6 + m = 25; m = 31

8.R-277 §8.R source ↗

In the following exercises, translate into an algebraic equation and solve.

Rochelle’s daughter is $11$ years old. Her son is $3$ years younger. How old is her son?

Answer

s = 11 − 3; 8 years old

8.R-279 §8.R source ↗

In the following exercises, translate into an algebraic equation and solve.

Peter paid $$9.75$ to go to the movies, which was $$46.25$ less than he paid to go to a concert. How much did he pay for the concert?

Answer

c − 46.25 = 9.75; $56.00

8.R-281 §8.R source ↗

In the following exercises, solve each equation using the Division Property of Equality.

$8 x = 72$

Answer

x = 9

8.R-283 §8.R source ↗

In the following exercises, solve each equation using the Division Property of Equality.

$0.25 p = 5.25$

Answer

p = 21

8.R-285 §8.R source ↗

In the following exercises, solve each equation using the Multiplication Property of Equality.

$\frac{n}{6} = 18$

Answer

n = 108

8.R-287 §8.R source ↗

In the following exercises, solve each equation using the Multiplication Property of Equality.

$36 = \frac{3}{4} x$

Answer

x = 48

8.R-289 §8.R source ↗

In the following exercises, solve each equation.

$−18 m = −72$

Answer

m = 4

8.R-291 §8.R source ↗

In the following exercises, solve each equation.

$0.45 x = 6.75$

Answer

x = 15

8.R-293 §8.R source ↗

In the following exercises, solve each equation.

$5 r -$ $3 r +$ $9 r =$ $35 -$ $2$

Answer

r = 3

8.R-295 §8.R source ↗

In the following exercises, solve the equations with constants on both sides.

$8 p + 7 = 47$

Answer

p = 5

8.R-297 §8.R source ↗

In the following exercises, solve the equations with constants on both sides.

$3 x + 19 = −47$

Answer

x = −22

8.R-299 §8.R source ↗

In the following exercises, solve the equations with variables on both sides.

$7 y = 6 y - 13$

Answer

y = −13

8.R-301 §8.R source ↗

In the following exercises, solve the equations with variables on both sides.

$k = −6 k - 35$

Answer

k = −5

8.R-303 §8.R source ↗

In the following exercises, solve the equations with constants and variables on both sides.

$12 x - 9 = 3 x + 45$

Answer

x = 6

8.R-305 §8.R source ↗

In the following exercises, solve the equations with constants and variables on both sides.

$4 u + 16 = −19 - u$

Answer

u = −7

8.R-307 §8.R source ↗

In the following exercises, solve each linear equation using the general strategy.

$6 (x + 6) = 24$

Answer

x = −2

8.R-309 §8.R source ↗

In the following exercises, solve each linear equation using the general strategy.

$- (s + 4) = 18$

Answer

s = −22

8.R-311 §8.R source ↗

In the following exercises, solve each linear equation using the general strategy.

$23 - 3 (y - 7) = 8$

Answer

y = 12

8.R-313 §8.R source ↗

In the following exercises, solve each linear equation using the general strategy.

$8 (r - 2) =$ $6 (r + 10)$

Answer

r = 38

8.R-315 §8.R source ↗

In the following exercises, solve each linear equation using the general strategy.

$4 (3.5 y + 0.25) =$ $365$

Answer

y = 26

8.R-317 §8.R source ↗

In the following exercises, solve each equation by clearing the fractions.

$\frac{2}{5} n - \frac{1}{10} = \frac{7}{10}$

Answer

n = 2

8.R-319 §8.R source ↗

In the following exercises, solve each equation by clearing the fractions.

$\frac{3}{4} a -$ $\frac{1}{3} =$ $\frac{1}{2} a +$ $\frac{5}{6}$

Answer

a = \frac{14}{3}

8.R-321 §8.R source ↗

In the following exercises, solve each equation by clearing the decimals.

$0.8 x -$ $0.3 =$ $0.7 x +$ $0.2$

Answer

x = 5

8.R-323 §8.R source ↗

In the following exercises, solve each equation by clearing the decimals.

$0.6 p -$ $1.9 =$ $0.78 p +$ $1.7$

Answer

p = −20

8.T-325 §8.T source ↗

Determine whether each number is a solution to the equation.
$3 x + 5 = 23 .$

ⓐ $6$

ⓑ $\frac{23}{5}$

Answer

ⓐ yes

ⓑ no

8.T-327 §8.T source ↗

In the following exercises, solve each equation.

$9 c = 144$

Answer

c = 16

8.T-329 §8.T source ↗

In the following exercises, solve each equation.

$−8 x -$ $15 +$ $9 x -$ $1 =$ $−21$

Answer

x = −5

8.T-331 §8.T source ↗

In the following exercises, solve each equation.

$\frac{2}{3} x = 6$

Answer

x = 9

8.T-333 §8.T source ↗

In the following exercises, solve each equation.

$10 y = −5 y + 60$

Answer

y = 4

8.T-335 §8.T source ↗

In the following exercises, solve each equation.

$9 m -$ $2 -$ $4 m +$ $m =$ $42 -$ $8$

Answer

m = 6

8.T-337 §8.T source ↗

In the following exercises, solve each equation.

$- (d + 9) = 23$

Answer

d = −32

8.T-339 §8.T source ↗

In the following exercises, solve each equation.

$2 (6 x + 5) -$ $8 =$ $−22$

Answer

x = −2

8.T-341 §8.T source ↗

In the following exercises, solve each equation.

$\frac{1}{4} p + \frac{1}{3} = \frac{1}{2}$

Answer

p = \frac{2}{3}

8.T-343 §8.T source ↗

In the following exercises, solve each equation.

Translate and solve: The difference of twice $x$ and $4$ is $16 .$

Answer

2x − 4 = 16; x = 10

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Problems and answers are adapted from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith and Andrea Honeycutt Mathis, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.