2 8 Solving AbsoluteValue Equations and Inequalities LEARNING

2 -8 Solving Absolute-Value Equations and Inequalities LEARNING GOALS FOR LESSON 2. 8 1. 2. Solve compound inequalities. Write and solve absolute-value equations and inequalities. disjunction Compound Inequality conjunction x ≤ – 3 OR x > 2 Set builder notation: {x|x ≤ – 3 U x > 2} x ≥ – 3 AND x < 2 Set builder notation: {x|x ≥ – 3 A disjunction is true if and only if at least one of its parts is true. n x < 2}. A conjunction is true if and only if all of its parts are true. Conjunctions can be written as a single statement as shown. x ≥ – 3 and x< 2 _________ LG 2. 8. 1 Solve the compound inequality. Then graph the solution set. 6 y < – 24 OR y + 5 ≥ 3 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3

2 -8 Solving Absolute-Value Equations and Inequalities Example 1 B: Solving Compound Inequalities Solve the compound inequality. Then graph the solution set. – 3 x < – 12 AND x + 4 ≤ 12 LG 2. 8. 1

2 -8 Solving Absolute-Value Equations and Inequalities Example 2 A: Solving Absolute-Value Equations Solve the equation. A. LG 2. 8. 2 |– 3 + k| = 10 B. C. |x + 9| = 13 Helpful Hint Think: Greator inequalities involving > or ≥ symbols are disjunctions. Think: Less thand inequalities involving < or ≤ symbols are conjunctions.

2 -8 Solving Absolute-Value Equations and Inequalities Example 3 A: Solving Absolute-Value Inequalities with Disjunctions Solve the inequality. Then graph the solution. A. |2 x + 1| ≥ 5 B. LG 2. 8. 2 |4 x| + 8 ≥ 16 Example 4 A: Solving Absolute-Value Inequalities with Conjunctions Solve the inequality. Then graph the solution. A. B. |3 x – 6| < 12 LG 2. 8. 2

2 -8 Solving Absolute-Value Equations and Inequalities Example 5: Absolute-Value Inequalities with No Solution and All Real Number Solutions Solve the compound inequality. Then graph the solution set. A. |3 x| + 36 > 12 B. C. -2|x| - 8 < 0 D. -8|x + 4| > 48 LG 2. 8. 2