Chapter 4 – Inequalities and Absolute Value 4.5 – Solving Absolute Value Inequalities

Today we will review: – Solving and graphing absolute value inequalities

4.5 – Solving Absolute Value Inequalities Absolute value inequality – has one of these forms: – | ax + b | < c – | ax + b | ≤ c – | ax + b | > c – | ax + b | ≥ c

4.5 – Solving Absolute Value Inequalities Graphing Inequalities – The graph of an absolute value inequality involving < or ≤ is a line segment. It can have open or solid dots Ex. | x | ≤ 3 means -3 ≤ x ≤ 3 – The graph of an absolute value inequality involving > or ≥ is two rays pointing in opposite directions It can have open or solid dots Ex. | x | > 4 means x 4

4.5 – Solving Absolute Value Inequalities Solving Absolute Value Inequalities | ax + b | < c | ax + b | ≤ c | ax + b | > c | ax + b | ≥ c Equivalent Form -c < ax + b < c -c ≤ ax + b ≤ c ax + b c ax + b ≤ -c OR ax + b ≥ c

4.5 – Solving Absolute Value Inequalities Example 1 – Solve | x + 3 | < 5. Then graph the solution.

4.5 – Solving Absolute Value Inequalities Example 2 – Solve | 2x – 5 | ≤ 9. Then graph the solution.

4.5 – Solving Absolute Value Inequalities Example 3 – Solve | 3x + 2 | ≥ 4. Then graph the solution.

4.5 – Solving Absolute Value Inequalities Example 4 – 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.

4.5 – Solving Absolute Value Inequalities HOMEWORK Page 201 #17 – 29, 48 – 50