Allday Education

Free Absolute Value Equations Worksheet

Ten absolute value equations, each with two solutions, plus an answer key listing both.

Answer key included
Name: Date:
Absolute Value Equations
1.
16=∣x−2∣16 = \left|x - 2\right|
2.
∣x−4∣=8\left|x - 4\right| = 8
3.
14=∣x+13∣14 = \left|x + 13\right|
4.
18=∣x−5∣18 = \left|x - 5\right|
5.
6=∣x+6∣6 = \left|x + 6\right|
6.
15=∣x−11∣15 = \left|x - 11\right|
7.
∣x+7∣=12\left|x + 7\right| = 12
8.
19=∣x+11∣19 = \left|x + 11\right|
9.
7=∣x+14∣7 = \left|x + 14\right|
10.
∣x+10∣=5\left|x + 10\right| = 5
Andy · alldayeverydaymath.com
Name: Answer KeyDate:
Absolute Value Equations
1.
16=∣x−2∣16 = \left|x - 2\right|
Answer: x=18 or x=−14x = 18 \text{ or } x = -14
2.
∣x−4∣=8\left|x - 4\right| = 8
Answer: x=12 or x=−4x = 12 \text{ or } x = -4
3.
14=∣x+13∣14 = \left|x + 13\right|
Answer: x=1 or x=−27x = 1 \text{ or } x = -27
4.
18=∣x−5∣18 = \left|x - 5\right|
Answer: x=23 or x=−13x = 23 \text{ or } x = -13
5.
6=∣x+6∣6 = \left|x + 6\right|
Answer: x=0 or x=−12x = 0 \text{ or } x = -12
6.
15=∣x−11∣15 = \left|x - 11\right|
Answer: x=26 or x=−4x = 26 \text{ or } x = -4
7.
∣x+7∣=12\left|x + 7\right| = 12
Answer: x=5 or x=−19x = 5 \text{ or } x = -19
8.
19=∣x+11∣19 = \left|x + 11\right|
Answer: x=8 or x=−30x = 8 \text{ or } x = -30
9.
7=∣x+14∣7 = \left|x + 14\right|
Answer: x=−7 or x=−21x = -7 \text{ or } x = -21
10.
∣x+10∣=5\left|x + 10\right| = 5
Answer: x=−5 or x=−15x = -5 \text{ or } x = -15
Andy · alldayeverydaymath.com

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About this worksheet

Every |x − a| = b equation splits into two cases, and forgetting the second case is the classic mistake. These problems are generated so both branches produce clean integer answers, making the two-case habit easy to check and grade.

Students shaky on the skill itself? Send them to the free lesson: Absolute Value Equations — explained step by step.

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