1. Indicator 10
Solving Inequalities

2. Addition and Subtraction Property of Inequality
Let a, b, and c be real numbers. If a > b, then a + c > b + c. If a < b, then a + c < b + c. This property is also true for ≥ and ≤. 5 > 4, so > Let a, b, and c be real numbers. If a > b, then a - c > b - c. If a < b, then a - c < b - c. This property is also true for ≥ and ≤. 5 > 4, so > 4 - 3

3. Example 1
What are the solutions of n – 5 < -3? Graph the solutions.

4. Example 2
What are the solutions of m – 11 ≥ -2? Graph the solutions

5. Example 3
What are the solutions of -1 ≥ y + 12? Graph the solutions.

6. Multiplication and Division Property of Inequality
Multiplication Property of Inequality: Let a, b, and c be real numbers with c > 0. If a > b, then ac > bc. If a < b, then ac < bc. Let a, b, and c be real numbers with c < 0. If a > b, then ac < bc. If a < b, then ac > bc. Division Property of Inequality: Let a, b, and c be real numbers with c > 0. If a > b, then a/c > b/c. If a < b, then a/c < b/c. Let a, b, and c be real numbers with c < 0. If a > b, then a/c < b/c. If a < b, then a/c > b/c.

7. Example 4:
What are the solutions of ? Graph the solutions.

8. Example 5:
What are the solutions of ? Graph and check

9. Example 6
What are the solutions of -5x ≥ -10? Graph the solution.