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)
Absolute value graph with solutionThe V-shaped graph of y = |ax + b| meets the horizontal level line y = c at the critical points; the highlighted part of the x-axis is the set of x values that satisfy the comparison.x-2-11234y = c

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