Absolute Value Inequalities 2222021 5 19 AM 2

Absolute Value Inequalities 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities 1

Definitions l Inequality is an equation where the variable does not equal to each other l >, <, or ≠ requires the dot being OPEN l >, <, or = required the dot being CLOSED 2/22/2021 5: 19 AM 2 -5: Graphing Linear Inequalities 2

Steps for Solving and Graphing Absolute Value Inequalities 1. Identify whether it is an AND/OR inequality 2. Write both equations with one with the regular sign and other equation with the sign SWITCHED with OPPOSITE number 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities 3

Solving for Absolute Value Inequalities When Solving for Inequalities, remember: Less Th. AND Great. OR Than Less Than, “AND” “OR” 2/22/2021 5: 19 AM Greater Than, 2 -8: Absolute Value Inequalities 4

Example 5 Solve -3 | – 8 2/22/2021 5: 19 AM and graph the solution -3 -3 | 0 2 -8: Absolute Value Inequalities | 2 5

Example 6 Solve | | | -5 – 9/2 -4 2/22/2021 5: 19 AM and graph the solution | 0 2 -8: Absolute Value Inequalities | 2 6

Example 7 Solve 2/22/2021 5: 19 AM and graph the solution 2 -8: Absolute Value Inequalities 7

Example 8 Solve 8

Example 8 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities 9

Example 10 Solve 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities 10

Example 11 Solve and graph the solution | 0 No Solution 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities 11

Your Turn Solve and graph the solution -2 -2 All Real Numbers 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities 12

Example 12 Solve and graph the solution | 0 All Real Numbers 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities 13

Your Turn Solve a number line and graph the solution on | | 0 4/3 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities | 6 14

Example 10 Solve 2/22/2021 5: 19 AM 2 -8: Absolute Value Inequalities 15