4.5 Solving Absolute Value Inequalities Solve and graph absolute value inequalities

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

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 < x < 3 What numbers are less than 3 units from 0 on a number line?

Example 2 Solve an absolute value inequality. You must think of the numbers that work in the absolute value x ≥ 4 x ≤ -4 or

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

Example 3 Solve an absolute value inequality. LITTLE IN THE MIDDLE < x <

Example 4 Solve an absolute value inequality A WHOLE BUNCH x < x > -4

Example 5 Solve an absolute value inequality A WHOLE BUNCH x ≤ x ≥ 4 x ≤ -5 x ≥ 2

Example 6 Solve an absolute value inequality. LITTLE IN THE MIDDLE ≤ 3x ≤ ≤ x ≤ 2

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 ≤ x ≤ 1.81 The scoop should be at or between 1.79 ounces and 1.81 ounces

Assignment pp Problems 13, 15, 17-20, odds, 34, 40, 43, 51-53