Absolute Value Solver

Solve absolute-value equations and inequalities

|1·x − 1| ≤ 2

Solution set

-1 ≤ x ≤ 3

Critical points

-1, 3

Vertex

(1, 0)

About this calculator

The Absolute Value Solver solves absolute-value equations and inequalities of the form |ax + b| = c, <, ≤, >, or ≥ c. It returns the exact solution set as points, an interval, or a union of rays, lists the critical points and vertex, and draws the V-shaped graph against the level line so you can see why. Use it for algebra homework and exam prep.

Common examples

|x| = 3 → x = −3 or x = 3
|x − 1| ≤ 2 → −1 ≤ x ≤ 3
|2x + 1| > 5 → x < −3 or x > 2
|x + 4| = −1 → no solution (an absolute value is never negative)
|x − 2| ≥ 0 → all real numbers