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Absolute Value Equations — Practice Problems

Practice solving absolute value equations. Each problem requires you to isolate the absolute value, split into two cases, and check for extraneous solutions. Click 'Show Answer' to see the full solution.

Quick Recap

For ∣A∣=c|A| = c where c≥0c \geq 0: set A=cA = c or A=−cA = -c and solve both. If c<0c < 0, there is no solution (absolute value is never negative). Always check your solutions in the original equation.

Practice Problems

1
Solve ∣x−3∣=7|x - 3| = 7.
2
Solve ∣2x+1∣=5|2x + 1| = 5.
3
Solve ∣x∣=−4|x| = -4.
4
Solve ∣3x−6∣=0|3x - 6| = 0.
5
Solve ∣x+5∣=2x+1|x + 5| = 2x + 1.
6
Solve 2∣x−1∣+3=112|x - 1| + 3 = 11.
7
Solve ∣4x∣=20|4x| = 20.
8
Solve ∣x−2∣=∣x+6∣|x - 2| = |x + 6|.
9
Solve ∣5−x∣=3|5 - x| = 3.
10
Solve ∣x2−9∣=0|x^2 - 9| = 0.

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