Solving Compound and Absolute Value Inequalities

1. Solving Compound and Absolute Value Inequalities Chapter 1 – Section 6

2. Compound Inequalities • Compound Inequality – a pair of inequalities joined by and or or • Ex: -1 < x and x ≤ 3 which can be written as -1 < x ≤ 3 • x < -1 or x ≥ 3 • For and statements the value must satisfy both inequalities • For or statements the value must satisfy one of the inequalities

3. And Inequalities • Graph the solution of 3x – 1 > -28 and 2x + 7 < 19. 3x > -27 and 2x < 12 x > -9 and x < 6

4. And Inequalities b)Graph the solution of -8 < 3x + 1 <19 -9 < 3x < 18 -3 < x < 6

5. Or Inequalities 3x < –12 –2x < 4 ALGEBRA 2 LESSON 1-4 Graph the solution of 3x + 9 < –3 or –2x + 1 < 5. 3x + 9 < –3 or –2x + 1 < 5 x < –4 or x > –2

6. Try These Problems • Graph the solution of 2x > x + 6 and x – 7 < 2 • x > 6 and x < 9 • Graph the solution of x – 1 < 3 or x + 3 > 8 • x < 4 or x > 11

7. Absolute Value Inequalities Let k represent a positive real number • │x │ ≥ k is equivalent to x ≤ -k or x ≥ k • │x │ ≤ k is equivalent to -k ≤ x ≤ k • Remember to isolate the absolute value before rewriting the problem with two inequalities

8. 2x < 2 2x > 8 Solve for x. Solve |2x – 5| > 3. Graph the solution. |2x – 5| > 3 2x – 5 < –3 or 2x – 5 > 3 Rewrite as a compound inequality. x < 1 or x > 4

9. Try This Problem Solve │2x - 3 │ > 7 2x – 3 > 7 or 2x – 3 < -7 2x > 10 or 2x < -4 x > 5 or x < -2

10. < < < < < – – – – – > > > – – – –2|x + 1| + 5 –3 –2|x + 1| –8 Isolate the absolute value expression. Subtract 5 from each side. |x + 1| 4 Divide each side by –2 and reverse the inequality. –4 x + 1 4 Rewrite as a compound inequality. –5 x 3 Solve for x. Solve –2|x + 1| + 5 –3. Graph the solution.

11. Try This Problem Solve |5z + 3| - 7 < 34. Graph the solution. |5z + 3| -7 < 34 |5z + 3| < 41 -41 < 5z + 3 < 41 -44 < 5z < 38 -44/5 < z < 38/5 -8 4/5 < z < 7 3/5

12. Homework p. 44 #27 - 40