1. 4.5 Solving Absolute Value Inequalities Solve and graph absolute value inequalities

2. Warm-up You have ten coins in your pocket. They are a mixture of quarters and dimes. If the total is $1.90, how many quarters and how many dimes do you have? Let x = number of quarters Let y = number of dimes You have 6 quarters and 4 dimes. Solve: |x – 4| = 23

3. An absolute value inequality has one of these forms: Example 1 Solve an absolute value inequality. You must think of the numbers that work in the absolute value. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -3< x < 3 What numbers are less than 3 units from 0 on a number line?

4. Example 2 Solve an absolute value inequality. You must think of the numbers that work in the absolute value. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 x ≥ 4 x ≤ -4 or

5. Solve an absolute value inequality. < or ≤ (less than) – LITTLE IN THE MIDDLE. > or ≥ (greater than) – A WHOLE BUNCH – ARMS GO OUT My Hint

6. Example 3 Solve an absolute value inequality. LITTLE IN THE MIDDLE. - 3 -3 -3 - 7 < x < 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

7. Example 4 Solve an absolute value inequality. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 A WHOLE BUNCH - 5 -5 x < -6 - 5 -5 x > -4

8. Example 5 Solve an absolute value inequality. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 A WHOLE BUNCH - 3 -3 2x ≤ -10 - 3 -3 2x ≥ 4 x ≤ -5 x ≥ 2

9. Example 6 Solve an absolute value inequality. LITTLE IN THE MIDDLE. - 6 -6 -6 - 18 ≤ 3x ≤ 6 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 3 3 3 - 6 ≤ x ≤ 2

10. Example 7 A spice scoop should contain 1.8 ounces with a tolerance of 0.01 ounce. Write and solve an absolute value inequality that describes the acceptable capacity for the scoop. Actual weightIdeal weightTolerance– ≤ LITTLE IN THE MIDDLE. +1.8 +1.8 +1.8 1.79 ≤ x ≤ 1.81 The scoop should be at or between 1.79 ounces and 1.81 ounces

11. Assignment pp. 201-203 Problems 13, 15, 17-20, 21-29 odds, 34, 40, 43, 51-53