Math Calculators

Absolute Value Equation Calculator

Solve an absolute value equation of the form |ax + b| = c for both possible values of x.

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About the Absolute Value Equation Calculator

An absolute value equation like |ax + b| = c has two possible solutions, because the expression inside the bars can equal either c or its negative. This splits the single equation into two ordinary linear equations that can each be solved directly.

Formula: ax + b = c or ax + b = −c, so x = (c − b) ÷ a or x = (−c − b) ÷ a

If c is negative, there is no solution, since an absolute value can never equal a negative number. This type of equation shows up often in algebra courses when working with distance, error tolerance and piecewise-defined expressions.