Absolute Value Equation Solver

Solution 1
Solution 2
Note

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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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.