Absolute Value Inequalities Calculator
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Solution
How to Use
- Enter the expression inside the absolute value bars (e.g., "2x + 3")
- Select the inequality operator (<, <=, >, >=)
- Enter the value on the right side of the inequality
- Click the "Solve Inequality" button
- The solution will be displayed below
Rules for Solving
For |ax + b| < c:
-c < ax + b < c
For |ax + b| <= c:
-c <= ax + b <= c
For |ax + b| > c:
ax + b < -c or ax + b > c
For |ax + b| >= c:
ax + b <= -c or ax + b >= c
Common Examples
| Inequality | Solution |
|---|---|
| |x + 2| < 5 | -7 < x < 3 |
| |2x - 1| <= 3 | -1 <= x <= 2 |
| |x - 3| > 2 | x < 1 or x > 5 |
| |3x + 2| >= 4 | x <= -2 or x >= 2/3 |
When to Use
- Solving mathematical problems
- Analyzing ranges of values
- Error analysis
- Distance problems
- Engineering calculations
Tips
- Enter expressions in the form "ax + b"
- Use proper mathematical notation
- Check your solution by plugging in test values
- Remember to reverse inequality signs when multiplying/dividing by negative numbers
- For complex expressions, simplify first
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