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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.

  • 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.

  • y + 2 = −6
  • a + \(\dfrac{1}{3} = \dfrac{5}{3}\)
  • 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 − \(\dfrac{3}{11} = \dfrac{9}{11}\)
  • p − 4.8 = 14

In the following exercises, solve the equation.

  • n − 12 = 32
  • y + 16 = −9
  • f + \(\dfrac{2}{3}\) = 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.

  • 13a = −65
  • 0.25p = 5.25
  • −y = 4

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

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

In the following exercises, solve each equation.

  • −18m = −72
  • \(\dfrac{c}{9}\) = 36
  • 0.45x = 6.75
  • \(\dfrac{11}{12} = \dfrac{2}{3} y\)
  • 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 − \(\dfrac{3}{8}\) = 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
  • \(\dfrac{5}{8} c\) − 4 = \(\dfrac{3}{8} c\) + 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
  • \(\dfrac{1}{3}\)(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.

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

  • \(\dfrac{23}{5}\)
  • n − 18 = 31
  • 4y − 8 = 16
  • −8x − 15 + 9x − 1 = −21
  • −15a = 120
  • \(\dfrac{2}{3}\)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
  • 2(6x + 5) − 8 = −22
  • 8(3a + 5) − 7(4a − 3) = 20 − 3a
  • \(\dfrac{1}{4} p + \dfrac{1}{3} = \dfrac{1}{2}\)
  • 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 and Attributions

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/[email protected] ."

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