1. Two-step Inequalities SOL 8.15 cont.

2. What is an inequality? An inequality is a mathematical sentence that compares expressions using: < less than > greater than ≤ less than or equal to ≥ greater than or equal to

3. Example 1: x/3 – 4 > 8 1. First, add 4 to both sides. 2. Multiply by 3 on both sides. 1. x/3 > 12 2. x > 36 so any number greater than 36 is a possible solution to this inequality

4. !!!!! Special rule !!!!! When you multiply or divide by a negative number, the inequality sign reverses. ( and ≤ becomes ≥)

5. Example 2: -2x + 4 ≤ 12 1. Subtract 4 from both sides. 2. Divide by -2 on both sides 1. -2x ≤ 8 2. x ≥ -4 the sign flips bc we divided by a negative number

6. Example 3: x/-6 – 8 > 3 1. Add 8 to both sides 2. Multiply by -6 on both sides 1. x/-6 > 11 2. x < -66 the sign flips bc we multiplied by a negative number

7. Graphing Inequalities If you have >, you place an “open” (unshaded) circle on the number and shade to the right, including the arrow. If you have <, you place an “open” (unshaded) circle on the number and shade to the left, including the arrow. If you have ≥, you place a “closed” (shaded) circle on the number and shade to the right, including the arrow. If you have ≤, you place a “closed” (shaded) circle on the number and shade to the left, including the arrow.

8. Graph the following x < -9 y ≥ 17 w ≤ -36 b > 4

9. Your turn! Solve the following inequalities, and then graph. 1. n/2 – 4 > -10 2. -2x + 4 ≤ 12 3. 19 ≥ 5x + 4 4. w/-2 + 8 < 16

10. Question you might see! Which is one value of the set of x that makes the following true? 7x + 3 > 17 A. 0 B. 1 C. 2 D. 3