1-6 Study Guide and Intervention Solving Compound and Absolute Value Inequalities Compound Inequalities A compound inequality consists of two inequalities joined by the word or the word To and or. solve a compound inequality, you must solve each part separately And Compound The graph is the intersection of solution Example: x > and x < 3 –4 sets of two inequalities. Inequalities Or Compound The graph is the union of solution sets of Example: x or x > 1 ≤ –3 Inequalities two inequalities. Example 1: Solve 2x + 5 19. –3 ≤ ≤ Graph the solution set on a number line. Example 2: Solve 3y 7 or 2y 1 –2 ≥ – ≤ –9. 2x + 5 and 2x + 5 19 –3 ≤ ≤ Graph the solution set on a number line. 2x 2x 14 –8 ≤ ≤ 7 x x 3y 2 7 or 2y 1 –4 ≤ ≤ – ≥ – ≤ –9 7 x 3y 9 or 2y –4 ≤ ≤ ≥ ≤ –8 3 or y y ≥ ≤ –4 Exercises Solve each inequality. Graph the solution set on a number line. 1. < 3x + 2 14 2. 3a + 8 < 23 or 6 > 7 a –10 ≤ – 3. 18 < 4x 10 < 50 4. 5k + 2 < or 8k 1 > 19 – –13 – 5. 100 5y 45 225 6. 2 > 10 or + 5 < b b ≤ – ≤ – –4 7. 22 < 6w < 82 8. 4d 1 > or 2d + 5 < 11 –2 – –9 1-6 Study Guide and Intervention (continued)
1-6 Study Guide and Intervention Solving Compound and Absolute Value Inequalities Compound Inequalities A 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 separately And Compound Inequalities The graph is the intersection of solution sets of two inequalities. Example: x > –4 and x < 3 Or Compound Inequalities The graph is the union of solution sets of two inequalities. Example: x ≤ –3 or x > 1 Example 1: Solve –3 ≤ 2x + 5 ≤ 19. Graph the solution set on a number line. –3 ≤ 2x + 5 and 2x + 5 ≤ 19 –8 ≤ 2x 2x ≤ 14 –4 ≤ x x ≤ 7 –4 ≤ x ≤ 7 Example 2: Solve 3y –2 ≥ 7 or 2y – 1 ≤ –9. Graph the solution set on a number line. 3y – 2 ≥ 7 or 2y – 1 ≤ –9 3y ≥ 9 or 2y ≤ –8 y ≥ 3 or y ≤ –4 Exercises Solve each inequality. Graph the solution set on a number line. 1. –10 < 3x + 2 ≤ 14 2. 3a + 8 < 23 or a – 6 > 7 3. 18 < 4x – 10 < 50 4. 5k + 2 < –13 or 8k – 1 > 19 5. 100 ≤ 5y – 45 ≤ 225 6. b – 2 > 10 or b + 5 < –4 7. 22 < 6w –2 < 82 8. 4d – 1 > –9 or 2d + 5 < 11 1-6 Study Guide and Intervention (continued)
1-6-Study_Guide_and_Intervention_Solving_Compound_and_Absolute_Value_Inequalities.docx