Absolute value equation solver
Solve supported absolute value equations with a constant, a linear expression, or another linear absolute value on the other side, then verify each candidate.
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The solver handles forms such as |2x - 5| = 9, |2x - 5| = x + 4, and |3x - 2| = |x + 6| when each expression inside an absolute value is linear.
Some equations such as |x| = x describe an interval rather than a finite list of roots. I leave those forms unsupported until the result model can represent interval solution sets accurately.
For |A| = B, I solve A = B and A = -B, then test the candidates in the original equation. When both sides are absolute values, I compare the inside expressions with the same sign and opposite signs.
The final substitution check is important when the expression on the other side contains x, because a candidate produced by one algebraic case may still fail the original absolute value equation.
Type or paste an equation, solve it, inspect the transformations, and use verification and the graph instead of relying on the final value alone.
|2x - 5| = 9|2x - 5| = x + 4|3x - 2| = |x + 6||x - 4| = -2Follow the same steps the calculator uses for three equations in this category.
x = -2, x = 7
Split the absolute value equation into its linear cases
|2*x-5|=9 → 2x-5=9 or 2x-5=-9
Verified
x = 1/3, x = 9
Split the absolute value equation into its linear cases
|2*x-5|=x+4 → 2x-5=x+4 or 2x-5=-x-4
Verified
x = -1, x = 4
Split the absolute value equation into its linear cases
|3*x-2|=|x+6| → 3x-2=x+6 or 3x-2=-x-6
Verified
Substitute each answer into the original equation and compare both sides.
Cubic and higher-degree polynomials, logarithmic, exponential, trigonometric, nested-radical, and multiple-absolute-value equations remain outside the supported solver scope.