Absolute Value Inequality Solver

About this calculator

Solving |ax + b| < c or |ax + b| > c means splitting the absolute value into its two cases based on the sign of the expression inside it. For a "less than" inequality, |ax+b| < c becomes the compound inequality −c < ax+b < c (only valid when c > 0), which solves to a single interval. For a "greater than" inequality, |ax+b| > c splits into two separate branches — ax+b > c or ax+b < −c — giving a solution that's the union of two disjoint rays rather than one interval.

This solver takes a, b, c, and the inequality direction, applies the correct case split, and returns the resulting solution interval or pair of rays, including edge cases like c ≤ 0 where the inequality is either always true or has no solution. Algebra and pre-calculus students use it to check homework and see the case-split reasoning applied to their specific numbers rather than just a final answer.