Absolute value equation solver
Enter a, b and c to get every solution of the equation. Handy for middle and high school algebra practice.
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How to use it
- Enter coefficient a, constant b and right side c.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
If c > 0 then ax + b = c or ax + b = -c, so x = (c - b)/a or x = (-c - b)/a. If c = 0 there is one solution x = -b/a; if c < 0 there is none.
Example
Inputs: Coefficient a = 2, Constant b = -3, Right side c = 5. Result: Solutions: x1 = 4, x2 = -1; Number of solutions: 2.
Limits and caveats
- Covers the form |ax + b| = c with a constant c only.
- Equations with two absolute values or x outside the bars are not supported.
Questions about this tool
Why are there usually two solutions?
Opposite numbers share the same absolute value, so the inside equals either c or -c.
When is there no solution?
When the right side is negative, since an absolute value is a distance and is never negative.
How do I solve |x| = 7?
Enter a = 1, b = 0, c = 7. The solutions are 7 and -7.