Lesson Worksheet: Solving Equations Containing Absolute Value Mathematics

In this worksheet, we will practice solving equations that include an absolute value.


Given that 𝑎>0, find the solution set of the equation |𝑥|+𝑎=0.

  • A{𝑎,𝑎}
  • B{𝑎}
  • C
  • D{𝑎}


What is the solution set of the equation |𝑥|=94?

  • A{94,94}
  • B{94}
  • C{95,95}
  • D{94}


What is the solution set of the equation 3|𝑥|66=0?

  • A{22}
  • B{22,22}
  • C{22}
  • D{66,66}


Write the set of all solutions to the equation |𝑥+6|=3.

  • A{9,9}
  • B{3,9}
  • C{9}
  • D{3,3}
  • E{9,3}


Solve |𝑥|+12=18.

  • A𝑥=6 or 𝑥=30
  • B𝑥=30 or 𝑥=30
  • C𝑥=18 or 𝑥=18
  • D𝑥=30 or 𝑥=6
  • E𝑥=6 or 𝑥=6


Find all possible values of 𝑥 given |||𝑥56|||=56.

  • A53
  • B53 or 0
  • C53 or 0
  • D32 or 16


Find all posssible values of 𝑥 given |||𝑥+12|||=34.

  • A54 or 54
  • B14 or 14
  • C14 or 54
  • D54 or 14


Evaluate |𝑎+9| for 𝑎=8.


What is the definition of |𝑛|, where 𝑛 is an integer?

  • AThe distance between 𝑛 and 0 on a number line
  • BThe distance between 𝑛 and 1 on a number line
  • C𝑛 rounded to the nearest even number
  • D𝑛 rounded to the nearest ten


Use the number line to order the points from greatest absolute value to least absolute value.

  • A𝐶, 𝐵, 𝐴
  • B𝐶, 𝐴, 𝐵
  • C𝐴, 𝐵, 𝐶
  • D𝐵, 𝐶, 𝐴
  • E𝐴, 𝐶, 𝐵

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