Absolute Value Equation Solver

About this calculator

An absolute value equation of the form |ax + b| = c is solved by splitting it into two linear cases, since the expression inside the bars can be either positive or negative and still produce the same absolute value: ax + b = c, or ax + b = −c. Each case is solved independently for x, giving up to two real solutions — unless c is negative, in which case there's no solution, since an absolute value can never equal a negative number.

This solver takes a, b, and c and returns every real solution to |ax + b| = c, showing the split into both cases. Algebra students and math teachers use it to check homework and verify that both branches of a solution were found correctly, since forgetting the negative case is one of the most common errors on this topic.