# 8.E: Solving Linear Equations (Exercises)

### 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.

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

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

- x + 7 = 19
- y + 2 = −6
- a + \(\frac{1}{3} = \frac{5}{3}\)
- n + 3.6 = 5.1

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

- u − 7 = 10
- x − 9 = −4
- c − \(\frac{3}{11} = \frac{9}{11}\)
- p − 4.8 = 14

In the following exercises, solve the equation.

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

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

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

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?
- Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?
- 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?
- 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.

- 8x = 72
- 13a = −65
- 0.25p = 5.25
- −y = 4

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

- \(\frac{n}{6}\) = 18
- y −10 = 30
- 36 = \(\frac{3}{4}\)x
- \(\frac{5}{8} u = \frac{15}{16}\)

In the following exercises, solve each equation.

- −18m = −72
- \(\frac{c}{9}\) = 36
- 0.45x = 6.75
- \(\frac{11}{12} = \frac{2}{3} y\)
- 5r − 3r + 9r = 35 − 2
- 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.

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

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

- 7y = 6y − 13
- 5a + 21 = 2a
- k = −6k − 35
- 4x − \(\frac{3}{8}\) = 3x

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

- 12x − 9 = 3x + 45
- 5n − 20 = −7n − 80
- 4u + 16 = −19 − u
- \(\frac{5}{8} c\) − 4 = \(\frac{3}{8} c\) + 4

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

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

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

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

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

### PRACTICE TEST

- Determine whether each number is a solution to the equation. 3x + 5 = 23.
- 6
- \(\frac{23}{5}\)

In the following exercises, solve each equation.

- n − 18 = 31
- 9c = 144
- 4y − 8 = 16
- −8x − 15 + 9x − 1 = −21
- −15a = 120
- \(\frac{2}{3}\)x = 6
- x + 3.8 = 8.2
- 10y = −5y + 60
- 8n + 2 = 6n + 12
- 9m − 2 − 4m + m = 42 − 8
- −5(2x + 1) = 45
- −(d + 9) = 23
- \(\frac{1}{3}\)(6m + 21) = m − 7
- 2(6x + 5) − 8 = −22
- 8(3a + 5) − 7(4a − 3) = 20 − 3a
- \(\frac{1}{4} p + \frac{1}{3} = \frac{1}{2}\)
- 0.1d + 0.25(d + 8) = 4.1
- Translate and solve: The difference of twice x and 4 is 16.
- 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?

### Contributors

Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."