Absolute Value Inequality Solver
How It Works
This absolute value inequality solver uses established formulas to provide accurate results.
The basic rule:
- |ax + b| < c → -c < ax+b < c
- | ax + b| > c → ax+b < -c OR ax+b > c
- < gives an interval (AND), > gives two rays (OR)
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is the difference between |x| < c and |x| > c?
|x| < c means x is within c units of 0, giving the interval (-c, c). |x| > c means x is more than c units from 0, giving x < -c or x > c. Less than = between, greater than = outside.
How do I solve an absolute value inequality?
For less-than: remove the absolute value and write a compound inequality -c < expression < c. For greater-than: split into two inequalities expression < -c OR expression > c. Then solve each.
What if the right side is negative?
If c < 0: |expression| < negative has no solution (absolute value is never negative). |expression| > negative is always true (absolute value is always ≥ 0).