Absolute Value Inequality Solver
Enter an absolute-value inequality of the form |ax + b| OP c. The solver handles the three regimes: c < 0 (always-true or always-false depending on direction), c = 0 (single-point and complement cases) and c > 0 (the standard compound or two-ray solution).
Frequently asked questions
How is |ax + b| < c rewritten?
As the compound inequality −c < ax + b < c, then solved for x. The result is a single bounded interval.
What about |ax + b| > c?
Two cases: ax + b > c or ax + b < −c. The result is the union of two rays.
What if c is negative?
|…| is never negative, so a < or ≤ inequality has no solution; a > or ≥ inequality is true for every x.