Comparing quantities
An inequality is a statement that two quantities are not equal. Instead of an equals sign, we use one of these symbols:
| > | greater than |
| < | less than |
| ≥ | greater than or equal to |
| ≤ | less than or equal to |
For example, 7 > 3 means 7 is greater than 3, and 2 < 5 means 2 is less than 5. The symbol always opens towards the larger number.
Key idea / Key idea
x ≥ 4 means x can be 4 or any number bigger than 4. x < 4 means x is any number smaller than 4, but not 4 itself.
Inequalities on a number line
We show an inequality using a number line. A closed circle (●) means the number is included (≥ or ≤). An open circle (○) means the number is not included (> or <). The arrow points in the direction of all the values that satisfy it.
Worked example / Worked example
Write an inequality for "a number x is at least 5".
"At least 5" means 5 or more, so x ≥ 5.
On a number line, draw a closed circle at 5 with an arrow pointing right.
Remember / Remember
- ≥ and ≤ include the boundary number.
- > and < do not include it.
- The symbol opens towards the larger value.