Absolute Value Equation
Solve absolute value equations of the form |ax + b| = c with step-by-step solutions. Free online absolute value equation solver with instant results.
About This Calculator
This absolute value equation calculator solves equations of the form |ax + b| = c. When c is positive, there are two solutions: ax + b = c and ax + b = -c. When c = 0, there is exactly one solution. When c is negative, there is no real solution.
Absolute value equations model a wide range of real-world scenarios including manufacturing tolerances, measurement errors, distance constraints, and boundary conditions in physics and engineering.
Frequently Asked Questions
How do you solve an absolute value equation?
To solve |ax + b| = c, rewrite as two equations: ax + b = c and ax + b = -c (when c >= 0). Solve each for x. If c < 0, there is no solution since absolute value cannot be negative.
What if c is negative in |ax + b| = c?
If c < 0, there is no real solution because absolute value is always non-negative. The equation |ax + b| = -5 has no real solutions.
What if c = 0 in |ax + b| = 0?
When c = 0, the equation |ax + b| = 0 has exactly one solution: x = -b/a. This is the point where the expression inside the absolute value equals zero.
What is an extraneous solution in absolute value equations?
An extraneous solution is a solution that satisfies a derived equation but not the original equation. In absolute value equations, always verify your solutions by substituting back into the original equation.
How are absolute value equations used in real life?
They model tolerance ranges in manufacturing (acceptable deviation from a specification), error margins in scientific measurements, distance tolerance in GPS navigation, and temperature variation ranges.
Is this tool free?
Yes, all calculators on Calculy are completely free to use with no registration required.