Absolute Value Equation Solver
Solve equations of the form |ax + b| = c for x.
| Root | Value |
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Request a ToolHow to Use the Absolute Value Equation Solver
This tool solves equations of the form |ax + b| = c.
- Enter coefficients. Provide the values for a, b, and c.
- View the solutions. The solver displays one or two solutions, or indicates when no solution exists (c is negative).
- Copy or share. Use the buttons to copy the result or share a pre-filled link.
About Absolute Value Equations
An absolute value equation |ax + b| = c has two cases: ax + b = c and ax + b = -c. When c is positive, there are two solutions. When c is zero, there is exactly one solution. When c is negative, there is no solution because absolute values are never negative. These equations are common in algebra courses and have practical applications in tolerance, distance, and error calculations.
Frequently Asked Questions
How many solutions does an absolute value equation have?
If c > 0, there are two solutions. If c = 0, there is one solution. If c < 0, there are no solutions.
Why can an absolute value never equal a negative number?
Absolute value measures the distance from zero on the number line. Distance is always zero or positive, so |expression| can never be negative.
How do I solve |ax + b| = c by hand?
Split into two equations: ax + b = c and ax + b = -c. Solve each for x. Check both solutions in the original equation.