1. CHAPTER 1 – EQUATIONS AND INEQUALITIES 1.6 – SOLVING COMPOUND AND ABSOLUTE VALUE INEQUALITIES Unit 1 – First-Degree Equations and Inequalities

2. 1.6 – Solving Compound and Absolute Value Inequalities In this section we will review:  Solving compound inequalities  Solving absolute value inequalities

3. 1.6 – Solving Compound and Absolute Value Inequalities Compound inequality – consists of two inequalities joined by the word and or the word or.  To solve a compound inequality, you must solve each part of the inequality The graph of a compound inequality containing and is the intersection of the solution sets of the two inequalities  Compound inequalities with and are called conjunctions  Compound inequalities with or are called disjunctions

4. 1.6 – Solving Compound and Absolute Value Inequalities A compound inequality containing the word and is true if and only if both inequalities are true  Example  x ≥ -1 and x < 2

5. 1.6 – Solving Compound and Absolute Value Inequalities Example 1  Solve 10 ≤ 3y – 2 < 19. Graph the solution set on a number line

6. 1.6 – Solving Compound and Absolute Value Inequalities The graph of a compound inequality containing or is the union of the solution sets of the two inequalities A compound inequality containing the word or is true if one or more of the inequalities is true  Example  x ≤ 1 or x > 4

7. 1.6 – Solving Compound and Absolute Value Inequalities Example 2  Solve x + 3 < 2 or –x ≤ -4. Graph the solution set on a number line.

8. 1.6 – Solving Compound and Absolute Value Inequalities An absolute value inequality can be solved by rewriting it as a compound inequality. For all real numbers a and b, b > 0, the following statements are true:  If |a| -b  If |2x + 1| -5  If |a| > b, then a > b OR a < -b  If |2x + 1| > 5, then 2x + 1 > 5 OR 2x + 1 < -5 These statements are also true for ≤ and ≥

9. 1.6 – Solving Compound and Absolute Value Inequalities Example 3  Solve |2x – 2| ≥ 4. Graph the solution set on a number line. Example 4  Solve |½ x – 5| - 8 ≥ -20. Graph the solution set on a number line

10. 1.6 – Solving Compound and Absolute Value Inequalities Example 5  Solve |3x -11| + 12 ≤ 10. Graph the solution set on a number line Example 6  Solve |5x| < 35. Graph the solution set on a number line

11. 1.6 – Solving Compound and Absolute Value Inequalities HOMEWORK Page 45 #12-20 (even), 24-30 (even), 34-38 (even)