1. Algebra 2 Chapter 1 Section 6 Objectives: 1.Solve compound inequalities 2.Solve absolute value inequalities Standards: A2.2.1c, A2.2.1d, and SMP 1,2,5,7,8

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 because the variable is between -1 and 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 a) Graph the solution of 3x – 1 > -28 and 2x + 7 < 19. 3x > -27 and 2x < 12 x > -9 and x < 6 b) Graph the solution of -8 < 3x + 1 <19 -9 < 3x < 18 -3 < x < 6

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

5. Try These Problems a) Graph the solution of 2x > x + 6 and x – 7 < 2 a) x > 6 and x < 9 b) Graph the solution of x – 1 8 a) x 11

6. Absolute Value Inequalities Let k represent a positive real number  │x │ ≥ k is equivalent tox ≤ -k or x ≥ k Same work as an “or” inequality  │x │ ≤ k is equivalent to-k ≤ x ≤ k Same work as an “and” inequality  Remember to isolate the absolute value before rewriting the problem with two inequalities

7. Solve |2x – 5| > 3. Graph the solution. (This is the same as doing an “or” compound inequality.) |2x – 5| > 3 2x – 5 3Rewrite as a compound inequality. x 4 2x 8 Solve for x.

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

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

10. Try This Problem Solve |5z + 3| - 7 < 34. Graph the solution. (This is the same as an “and” inequality.) |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

11. Ranges in Measurement  Absolute value inequalities and compound inequalities can be used to specify an allowable range in measurement.

12. Margin of Error 

13. The area A in square inches of a square photo is required to satisfy 8.5 ≤ A ≤ 8.9. Write this requirement as an absolute value inequality. Write an inequality.–0.2 A – 8.7 0.2 < – < – Rewrite as an absolute value inequality.|A – 8.7| 0.2 < – Find the difference margin for the area boundaries. 8.9 – 8.5 2 = 0.4 2 = 0.2Find the average of the maximum and minimum values. 8.9 + 8.5 2 = 17.4 2 = 8.7

14. Try This Problem The specification for the circumference C in inches of a basketball for junior high school is 27.75 ≤ C ≤ 30. Write the specification as an absolute value inequality. Find the difference margin. Find the average from min and max values. Write the absolute value inequality.

15. Homework  Practice 1.6 Pages 45-48 #13-51 odd