Absolute Value Equation Solver — |ax + b| = c (Free)
Use this free absolute value equation solver to solve equations of the form |ax + b| = c. Enter a, b and c and you’ll get both solutions (or a clear note when there’s one or none), with each case worked out step by step.
How to use the solver
- Enter the coefficients a and b inside the absolute value, and the value c on the right.
- Press Calculate.
- Read the solution(s) and the two-case working.
Why there are two cases
Because absolute value measures distance, |ax + b| = c (with c > 0) splits into two equations: ax + b = c and ax + b = −c. If c = 0 there is exactly one solution, and if c < 0 there is none, since absolute value can’t be negative.
Frequently asked questions
Why does |ax + b| = c have two solutions?
Because the expression inside can be either +c or −c and still have the same absolute value, giving two linear equations to solve.
What if c is negative?
There is no solution: an absolute value is always zero or positive, so it can never equal a negative number.
What if c is zero?
There is exactly one solution, found by solving ax + b = 0.
Read the full lesson: learn the method step by step.
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