Absolute Value Inequality Solver

Easily solve absolute value inequalities of the form |ax + b| < c, |ax + b| > c, |ax + b| ≤ c, or |ax + b| ≥ c. Get step-by-step solutions and visual representation on a number line.

Enter Absolute Value Inequality:

Example formats: |2x - 1| < 5, |3x + 2| >= 7.

Solution Set:

Number Line Visualization

Understanding Absolute Value Inequalities

Absolute value inequalities are inequalities that involve the absolute value of an algebraic expression. The absolute value of a number is its distance from zero on the number line, and it's always non-negative. Solving absolute value inequalities involves finding the range of values that satisfy the inequality. For example, to solve |x| < 3, we need to find all x values whose distance from zero is less than 3, which is -3 < x < 3. Similarly, for |x| > 3, the solution is x < -3 or x > 3. This tool helps you solve inequalities of the form |ax + b| < c, > c, ≤ c, or ≥ c, providing both the solution set and a visual representation on a number line.