## 6.5 Outline

- Comparison property
- Solving linear inequalities
- inequality symbol
- inequality
- addition property of inequality
- multiplication property of inequality
- procedure for solving a linear inequality

## 6.5 Essential Ideas

**Comparison Property**

For any two numbers *x* and *y*, exactly one of the following is true:

*x = y,**x*is equal to*y*(the same as)*x > y, x*is greater than*y*(larger than)*x < y, x*is less than*y*(smaller than).

Given *x < y, x ≤ y, x > y, * or *x ≥ y*:

The **inequality symbols are the same **if you

- add the same number to both side.
- subtract the same number from both sides.
- multiply both sides by a positive number.
- divide both sides by a positive number.

The **inequality symbols are reversed **if you

- 1. multiply both sides by a negative number.
- divide both sides by a negative number.
- interchange the
*x*and*y.*