Lesson Worksheet: Solving Equations Containing Absolute Value Mathematics

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

Q1:

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

  • A{−𝑎,𝑎}
  • B{−𝑎}
  • C∅
  • D{𝑎}

Q2:

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

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

Q3:

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

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

Q4:

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}

Q5:

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

Q6:

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

  • A−53
  • B53 or 0
  • C−53 or 0
  • D32 or −16

Q7:

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

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

Q8:

Evaluate |𝑎+9| for 𝑎=−8.

Q9:

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

Q10:

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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