Math Calculators

Absolute Value Inequalities Calculator

Solve an absolute value inequality of the form |ax + b| < c or |ax + b| > c and get the solution in interval form.

Lower bound —

Upper bound —

Solution —

About the Absolute Value Inequalities Calculator

Absolute value inequalities split into two cases depending on the direction of the inequality. A "less than" inequality describes values trapped between two bounds, while a "greater than" inequality describes values outside those bounds.

Formula: |ax + b| < c → −c < ax + b < c. |ax + b| > c → ax + b < −c or ax + b > c

Solving each piece for x produces the lower and upper bounds shown above, which combine into the final interval notation. These inequalities are common in error-margin and tolerance problems.