What Is an Inequality in Math?
An inequality is a mathematical statement that two values are not necessarily equal, one may be greater than, less than, or at most/at least equal to the other.
The four inequality symbols
| Symbol | Meaning | Example |
|---|---|---|
| > | greater than | 8 > 5 |
| < | less than | 3 < 10 |
| ≥ | greater than or equal to | x ≥ 4 |
| ≤ | less than or equal to | x ≤ 10 |
Memory trick: The open end of the symbol always faces the larger value. Think of it as a hungry alligator that always eats the bigger number.
Equations vs. inequalities
- Equation: x + 3 = 7 → one answer: x = 4
- Inequality: x + 3 > 7 → many answers: x can be 5, 6, 7, 100, 4.1...
Equations have one solution. Inequalities have a range of solutions.
Real-world examples
- "You must be at least 48 inches tall" → height ≥ 48
- "No more than 20 items" → items ≤ 20
- "The temperature is below freezing" → temp < 32°F
Related concepts
- How to Teach Inequalities: full teaching guide
- Variables and equations: solving with equal signs
- Comparing numbers: the foundation of inequality thinking