Absolute Value Equation Calculator
Solve |ax + b| = c for real x, with a nonzero and c nonnegative.
Formula
x = (c − b)/a or (−c − b)/a
Smaller root ≈ min((7),(-1)) · Larger root ≈ max((7),(-1))
How to use
- Enter a nonzero coefficient a.
- Enter b and a nonnegative c.
- Read the two ordered roots; equal values mean one root.
Examples
- |2x − 6| = 8 gives x = −1 or 7.
Frequently asked questions
Why must a be nonzero?
Otherwise x disappears and the equation has either no solution or every real number as a solution.
What if c is zero?
Both displayed roots coincide at −b/a.
What if c is negative?
An absolute value cannot be negative, so there is no real solution. This form accepts c ≥ 0.
Sources
Updated: