1. 2.5-2 – Absolute Value Inequalities and their graphs

2. Absolute Value Inequalities
Recall, with absolute value inequalities…
|x| > a means we solve x > a OR x < -a
|x| < a means we solve –a < x < a
We do the same with graphing absolute value inequalities

3. AND/OR distinction OR = all areas AND = only overlapping areas
Use 2 colors when possible (or more)
The same rules for shading and types of lines still apply

4. Example. Graph the solutions sets to the inequalities |2x – 4| ≥ 4

5. Example. Graph the absolute value inequalities | y – 2 | > 5.

6. Joint Conditions Possible to have multiple absolute value inequalities
Treat as 2 separate problems
1) Graph each inequality
2) Determine the solution “overlap” asked for (IE, is it an AND/OR)

7. Example. Graph the solution set to the joint inequalities |x – 3| > 1 AND |y – 3| ≤ 4

8. Word Problems
Example. You run a small t-shirt business. Each month, you have fixed costs of $400. Your variable costs are $4.00 per t-shirt produced and you must spend no more than $2,000 a month to make a profit. Write a inequality to model the situation.

9. Assignment Pg
30-39 odd, all