1. October 31, 2012 Solving Absolute Value Inequalities DO NOW: Solve. 1. 2. │x + 13│ = 8 3. │3x – 9│= -24 HW 6.5b: Pg. 350 #29- 39, skip 36 and 38 Unit Test Monday, Nov 5

2. Lesson 6.5b Solving Absolute Value Inequalities with >, ≥ (greater) Example 1: Graph the values for x that will satisfy the inequality. Then solve. │x│≥ 3 5 -4-2024 -5 -315-53 “All values of x whose distance is 3 or more units away from zero.” Try |x| > 5

3. Solving Absolute Value Inequalities with <, ≤ (less than) Example 2: Graph the values for x that will make this true. Then solve. | x | ≤ 3 5 -4-2024 -5 -315-53 “All values of x whose distance is 3 or less units away from zero.” Try |x| < 5

4. Solving Absolute Value Inequalities Example 3) Solve, then graph |3x -12| ≥ 6 * Flip the inequality for the negative case. 20 -15-5515 -20 -1010-20200 Use the same steps you used to solve for Absolute Value Equations! Set up 2 equations: each for the positive and negative solutions

5. This these! 1.Solve and graph |2x + 3| < 15 Step 1: Take the inside value and set the two cases, the positive and negative (flip the <) Step 2: Graph the answer. Step 3: Write the solution

6. 2. Solve and graph |x – 4| ≥ 10 20 -15-5515 -20 -1010-20200 Step 1: Take the inside value and set the two cases, the positive and negative (flip the ≥) Step 2: Graph the answer. Step 3: Write the solution

7. The difference between |x| > n and |x| < n |x| ≥ n (greater than) is n distance or more away from zero and an “OR” compound inequality. graph OUT │x│ ≤ n (less than) is within n distance from zero and an “AND” compound inequality. graph IN

8. Start practicing on your homework. HW 6.5b: Pg. 350 #29-39, skip 36 and 38