Absolute Value Equation Solver
How It Works
This absolute value equation solver uses established formulas to provide accurate results.
The basic rule:
- |ax + b| = c
- Case 1: ax + b = c → x = (c - b)/a
- Case 2: ax + b = -c → x = (-c - b)/a
- No solution if c < 0
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
Why are there two solutions to an absolute value equation?
Absolute value measures distance from zero, so |expression| = c means the expression equals either c or -c. This creates two separate linear equations to solve.
When does an absolute value equation have no solution?
When c is negative. Since absolute value is always non-negative (≥ 0), |anything| = negative number is impossible.
How do I check my answers?
Substitute each solution back into the original equation and verify that both sides are equal. Sometimes one solution may be extraneous if the original problem had restrictions.