Chapter 4 – Inequalities and Absolute Value

4.5 – Solving Absolute Value Inequalities

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 or 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 OR 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

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