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|x-2|=5 asks 'which xx is distance 5 from 2?' — two answers.

Showing a random 20 of 50 problems.

Example 1

medium
Solve ∣2x+1∣=∣x−2∣|2x+1|=|x-2|.

Example 2

easy
Solve ∣x+6∣=0|x+6|=0.

Example 3

medium
Solve ∣4−2x∣=6|4-2x|=6.

Example 4

medium
Solve 2∣x−1∣=102|x-1|=10.

Example 5

easy
Solve ∣x−10∣=0|x-10|=0.

Example 6

easy
Solve ∣x−3∣=2|x-3|=2.

Example 7

hard
Solve ∣x2−5∣=4|x^2-5|=4.

Example 8

medium
Solve 3∣x−2∣=153|x-2|=15.

Example 9

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

Example 10

medium
Solve ∣x+2∣3=4\frac{|x+2|}{3}=4.

Example 11

medium
Solve ∣x−4∣+3=8|x-4|+3=8.

Example 12

easy
Solve ∣x∣=−4|x|=-4.

Example 13

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

Example 14

medium
Solve ∣5−x∣=2|5-x|=2.

Example 15

medium
Solve ∣3x+1∣=10|3x+1|=10.

Example 16

easy
Solve ∣x∣=0|x|=0.

Example 17

medium
Solve ∣x+2∣=−3|x + 2| = -3.

Example 18

easy
Solve ∣x+1∣=4|x+1|=4.

Example 19

medium
Solve ∣2x+1∣=5|2x + 1| = 5.

Example 20

medium
Solve 4∣x∣−1=114|x|-1=11.
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