
# 8.E: Solving Linear Equations (Exercises)

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## 8.1 - Solve Equations using the Subtraction and Addition Properties of Equality

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

1. x + 16 = 31, x = 15
2. w − 8 = 5, w = 3
3. −9n = 45, n = 54
4. 4a = 72, a = 18

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

1. x + 7 = 19
2. y + 2 = −6
3. a + $$\frac{1}{3} = \frac{5}{3}$$
4. n + 3.6 = 5.1

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

1. u − 7 = 10
2. x − 9 = −4
3. c − $$\frac{3}{11} = \frac{9}{11}$$
4. p − 4.8 = 14

In the following exercises, solve the equation.

1. n − 12 = 32
2. y + 16 = −9
3. f + $$\frac{2}{3}$$ = 4
4. d − 3.9 = 8.2
5. y + 8 − 15 = −3
6. 7x + 10 − 6x + 3 = 5
7. 6(n − 1) − 5n = −14
8. 8(3p + 5) − 23(p − 1) = 35

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

1. The sum of −6 and m is 25.
2. Four less than n is 13.

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

1. Rochelle’s daughter is 11 years old. Her son is 3 years younger. How old is her son?
2. Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?
3. 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?
4. Elissa earned $152.84 this week, which was$21.65 more than she earned last week. How much did she earn last week?

## 8.2 - Solve Equations using the Division and Multiplication Properties of Equality

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

1. 8x = 72
2. 13a = −65
3. 0.25p = 5.25
4. −y = 4

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

1. $$\frac{n}{6}$$ = 18
2. y −10 = 30
3. 36 = $$\frac{3}{4}$$x
4. $$\frac{5}{8} u = \frac{15}{16}$$

In the following exercises, solve each equation.

1. −18m = −72
2. $$\frac{c}{9}$$ = 36
3. 0.45x = 6.75
4. $$\frac{11}{12} = \frac{2}{3} y$$
5. 5r − 3r + 9r = 35 − 2
6. 24x + 8x − 11x = −7−14

## 8.3 - Solve Equations with Variables and Constants on Both Sides

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

1. 8p + 7 = 47
2. 10w − 5 = 65
3. 3x + 19 = −47
4. 32 = −4 − 9n

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

1. 7y = 6y − 13
2. 5a + 21 = 2a
3. k = −6k − 35
4. 4x − $$\frac{3}{8}$$ = 3x

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

1. 12x − 9 = 3x + 45
2. 5n − 20 = −7n − 80
3. 4u + 16 = −19 − u
4. $$\frac{5}{8} c$$ − 4 = $$\frac{3}{8} c$$ + 4

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

1. 6(x + 6) = 24
2. 9(2p − 5) = 72
3. −(s + 4) = 18
4. 8 + 3(n − 9) = 17
5. 23 − 3(y − 7) = 8
6. $$\frac{1}{3}$$(6m + 21) = m − 7
7. 8(r − 2) = 6(r + 10)
8. 5 + 7(2 − 5x) = 2(9x + 1) − (13x − 57)
9. 4(3.5y + 0.25) = 365
10. 0.25(q − 8) = 0.1(q + 7)

## 8.4 - Solve Equations with Fraction or Decimal Coefficients

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

1. $$\frac{2}{5} n − \frac{1}{10} = \frac{7}{10}$$
2. $$\frac{1}{3} x + \frac{1}{5} x = 8$$
3. $$\frac{3}{4} a − \frac{1}{3} = \frac{1}{2} a + \frac{5}{6}$$
4. $$\frac{1}{2}$$(k + 3) = $$\frac{1}{3}$$(k + 16)

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

1. 0.8x − 0.3 = 0.7x + 0.2
2. 0.36u + 2.55 = 0.41u + 6.8
3. 0.6p − 1.9 = 0.78p + 1.7
4. 0.10d + 0.05(d − 4) = 2.05

## PRACTICE TEST

1. Determine whether each number is a solution to the equation. 3x + 5 = 23.
1. 6
2. $$\frac{23}{5}$$

In the following exercises, solve each equation.

1. n − 18 = 31
2. 9c = 144
3. 4y − 8 = 16
4. −8x − 15 + 9x − 1 = −21
5. −15a = 120
6. $$\frac{2}{3}$$x = 6
7. x + 3.8 = 8.2
8. 10y = −5y + 60
9. 8n + 2 = 6n + 12
10. 9m − 2 − 4m + m = 42 − 8
11. −5(2x + 1) = 45
12. −(d + 9) = 23
13. $$\frac{1}{3}$$(6m + 21) = m − 7
14. 2(6x + 5) − 8 = −22
15. 8(3a + 5) − 7(4a − 3) = 20 − 3a
16. $$\frac{1}{4} p + \frac{1}{3} = \frac{1}{2}$$
17. 0.1d + 0.25(d + 8) = 4.1
18. Translate and solve: The difference of twice x and 4 is 16.
19. Samuel paid $25.82 for gas this week, which was$3.47 less than he paid last week. How much did he pay last week?