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Homework: Absolute Value Equations

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems related to absolute value equations.

Exercise 1

∣ x ∣ = 5 ∣ x ∣ = 5 size 12{ lline x rline =5} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 2

∣ x ∣ = 0 ∣ x ∣ = 0 size 12{ lline x rline =0} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 3

∣ x ∣ = − 2 ∣ x ∣ = − 2 size 12{ lline x rline = - 2} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 4

10 ∣ x ∣ = 5 10 ∣ x ∣ = 5 size 12{"10" lline x rline =5} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 5

∣ x + 3 ∣ = 1 ∣ x + 3 ∣ = 1 size 12{ lline x+3 rline =1} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 6

4 ∣ x − 2 ∣ 3 = 2 4 ∣ x − 2 ∣ 3 = 2 size 12{ { {4 lline x - 2 rline } over {3} } =2} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 7

7 ∣ 2x + 3 ∣ − 4 = 4 7 ∣ 2x + 3 ∣ − 4 = 4 size 12{7 lline 2x+3 rline - 4=4} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 8

∣ 2x − 3 ∣ = x ∣ 2x − 3 ∣ = x size 12{ lline 2x - 3 rline =x} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 9

∣ 2x + 2 ∣ = x ∣ 2x + 2 ∣ = x size 12{ lline 2x+2 rline =x} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Exercise 10

∣ x − 5 ∣ = 2x − 7 ∣ x − 5 ∣ = 2x − 7 size 12{ lline x - 5 rline =2x - 7} {}

  • a. Solve for xx size 12{x} {}
  • b. Check your answer(s) in the original equation.

Check-yourself hint:

For exercises 8, 9, and 10, one of them has no valid solutions, one has one valid solution, and one has two valid solutions.

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