Solve an Absolute Value Equation with Fractions

Published on October 7, 2026

Algebra

Solve |(5x−1)/2| = |(3x+1)/4| by multiplying both sides by 4, then considering equal and opposite expressions inside the absolute values. The solutions are x = 3/7 and x = 1/13.

Question

Solve #15 please step by step

Answer

Multiply both sides by :
Set the expressions inside the absolute values equal, then opposite:

Theorems

• Absolute Value Equality Property

For real numbers

and

if and only if

. In this problem, set the expressions inside the absolute values equal and opposite.

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