Practice Absolute Value Equations in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Absolute value equations solve for values whose distance from zero or another number matches a target amount.

An absolute-value equation is a distance problem — ∣x−2∣=5 asks 'which x is distance 5 from 2?' — two answers.

Showing a random 20 of 50 problems.

Example 1

medium
Solve ∣2x+1∣=∣x−2∣.

Example 2

easy
Solve ∣x+6∣=0.

Example 3

medium
Solve ∣4−2x∣=6.

Example 4

medium
Solve 2∣x−1∣=10.

Example 5

easy
Solve ∣x−10∣=0.

Example 6

easy
Solve ∣x−3∣=2.

Example 7

hard
Solve ∣x2−5∣=4.

Example 8

medium
Solve 3∣x−2∣=15.

Example 9

medium
What is the sum of all solutions of ∣2x−6∣=8?

Example 10

medium
Solve ∣x+2∣3=4.

Example 11

medium
Solve ∣x−4∣+3=8.

Example 12

easy
Solve ∣x∣=−4.

Example 13

easy
Fill in: ∣x−a∣=b (with b>0) has solutions x=a+b or x= ____.

Example 14

medium
Solve ∣5−x∣=2.

Example 15

medium
Solve ∣3x+1∣=10.

Example 16

easy
Solve ∣x∣=0.

Example 17

medium
Solve ∣x+2∣=−3.

Example 18

easy
Solve ∣x+1∣=4.

Example 19

medium
Solve ∣2x+1∣=5.

Example 20

medium
Solve 4∣x∣−1=11.
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