Using the Absolute Value Equation Calculator
An absolute value measures distance from zero. A positive target usually produces two branches, while a zero target produces one. This tool solves a single absolute-value expression equal to a constant, not nested expressions or inequalities.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- a in |ax + b|
- 2
- b in |ax + b|
- -3
- c (absolute-value target)
- 7
Example result
- Solution
- x = 5 or x = -2
- Number of real solutions
- 2
- Verification
- Each branch makes the absolute value equal to the target.
- Steps
- Split |2x + (-3)| = 7 into two branches. Branch 1: 2x + (-3) = 7, so x = 5. Branch 2: 2x + (-3) = -7, so x = -2. Both branches satisfy the original absolute-value equation.
Method and assumptions
For a nonnegative target, solve ax+b=c and ax+b=−c. Remove duplicate roots when c=0. A negative target has no real solution; a zero coefficient is checked as a constant equation. Integer inputs only.
Reference: openstax.org — method and further reading
Check the answer in the original problem
After solving, substitute the result into the original equation or relationship where possible. This can catch a sign error or a coefficient entered in the wrong position. Keep the exact inputs available when comparing with another tool, since changing a coefficient or rounding an intermediate value can change the problem being solved.
Common question
Why are there two roots?
The expression inside the bars may equal the positive target or its negative. Solve both linear branches. When the target is zero, the two branches produce the same root.