1. Warm-Up Exercises 1. Solve |x – 6| = 4. 2. Solve |x + 5| – 8 = 2. ANSWER 2, 10 ANSWER –15, 5

2. Warm-Up Exercises 3. A frame will hold photographs that are 5 inches by 8 inches with an absolute deviation of 0.25 inch for length and width. What are the minimum and maximum dimensions for photos? ANSWER min: 4.75 in. by 7.75 in. ; max: 5.25 in. by 8.25 in.

3. Warm-Up Exercises Solve absolute value inequalities EXAMPLE 1 Solve the inequality. Graph your solution. a.a. |x| ≥ 6 a.a. The distance between x and 0 is greater than or equal to 6. So, x ≤ –6 or x ≥ 6. SOLUTION ANSWER The solutions are all real numbers less than or equal to –6 or greater than or equal to 6.

4. Warm-Up Exercises Solve absolute value inequalities EXAMPLE 1 b.b. |x| ≤ 5|x| ≤ 5 The distance between x and 0 is less than or equal to 0.5. So, –0.5 ≤ x ≤ 0.5. SOLUTION Solve the inequality. Graph your solution. ANSWER The solutions are all real numbers greater than or equal to –0.5 and less than or equal to 0.5.

5. Warm-Up Exercises x ≤ –8 or x ≥ 8 Find a base using the percent equation EXAMPLE 4 GUIDED PRACTICE for Example 1 Solve the inequality. Graph your solution. 1. |x| ≥ 8 ANSWER

6. Warm-Up Exercises Find a base using the percent equation EXAMPLE 4 GUIDED PRACTICE for Example 1 2. |u| < 3.5 Solve the inequality. Graph your solution. –3.5 < u < 3.5 ANSWER

7. Warm-Up Exercises Find a base using the percent equation EXAMPLE 4 GUIDED PRACTICE for Example 1 3. v > 2 3 Solve the inequality. Graph your solution. 2 3 2 3 v ANSWER

8. Warm-Up Exercises EXAMPLE 2 Solve an absolute value inequality Solve x – 5 ≥ 7. Graph your solution. Write original inequality. | x – 5 | ≥ 7 x – 5 ≤ −7 or x – 5 ≥ 7 Rewrite as compound inequality. x ≤ –2 or x ≥ 12 Add 5 to each side. ANSWER The solutions are all real numbers less than or equal to –2 or greater than or equal to 12. Check several solutions in the original inequality.

9. Warm-Up Exercises EXAMPLE 3 Solve an absolute value inequality Solve |–4x – 5| + 3 < 9. Graph your solution. |–4x – 5| + 3 < 9 –6 < –4x – 5 < 6 |–4x – 5| < 6 –1 < –4x < 11 0.25 > x > –2.75 –2.75 < x < 0.25 Write original inequality. Subtract 3 from each side. Rewrite as compound inequality. Add 5 to each expression. Rewrite in the form a < x < b. Divide each expression by –4. Reverse inequality symbol.

10. Warm-Up Exercises EXAMPLE 3 Solve an absolute value inequality ANSWER The solutions are all real numbers greater than –2.75 and less than 0.25.

11. Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 6.3 5m – 6 – 8 13 < – Solve the inequality. Graph your solution. –0.2 ≤ m ≤ 2.6 ANSWER

12. Warm-Up Exercises EXAMPLE 4 Solve a multi-step problem Computers You are buying a new computer and find 10 models in a store advertisement. The prices are $890, $750, $650, $370, $660, $670, $450, $650, $725, and $825. Find the mean of the computer prices. You are willing to pay the mean price with an absolute deviation of at most $100. How many of the computer prices meet your condition ?

13. Warm-Up Exercises EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Find the mean by dividing the sum of the prices by 10. = 6640 10 = 664 Mean = 890 + 750 + 650 + 370 + 660 + 670 + 450 + 650 + 725 + 825 10

14. Warm-Up Exercises EXAMPLE 4 Solve a multi-step problem STEP 2 Write and solve an inequality. An absolute deviation of at most $100 from the mean, $664, is given by the inequality x – 664 ≤ 100. Write absolute value inequality. x – 664 ≤ 100 – 100 ≤ x – 664 ≤ 100 Write as compound inequality. 564 ≤ x ≤ 764 Add 664 to each expression.

15. Warm-Up Exercises EXAMPLE 4 Solve a multi-step problem ANSWER The prices you will consider must be at least $564 and at most $764. Six prices meet your condition: $750, $650, $660, $670, $650, and $725.

16. Warm-Up Exercises GUIDED PRACTICE for Example 4 7. WHAT IF? In Example 4, suppose that you are willing to pay the mean price with an absolute deviation of at most $75. How many of the computer prices meet this condition? ANSWER 5 computer prices

17. Warm-Up Exercises Warm-up: Homework: Page 343 #3-20 all

18. Warm-Up Exercises Daily Homework Quiz Solve the inequality. Graph your solution. 1. | x – 5 | > 3 ANSWERall real numbers less than 2 or greater than 8

19. Warm-Up Exercises Daily Homework Quiz 2. | x + 3 | + 6 ≤ 8 ANSWERall real numbers greater than or equal to –5 and less than or equal to –1 Solve the inequality.Graph your solution.

20. Warm-Up Exercises GUIDED PRACTICE Solve the inequality. Graph your solution. x + 3 > 8 3. x < –11 or x > 5 ANSWER 2w – 1 < 11 4. ANSWER –5 < w < 6

21. Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 2w – 1 < 11 5. Solve the inequality. Graph your solution. ANSWER –5 < w < 6

22. Warm-Up Exercises Daily Homework Quiz The clock in your car has an absolute deviation of at most 4 minutes after 6 months. After 6 months, the clock reads 7:38. Write and solve an inequality to find the possible times. 3. ANSWER | x – 7:38 | ≤ 4; from 7:34 through 7:42