2.5-2 – Absolute Value Inequalities and their graphs

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

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

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

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

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)

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

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.

Assignment Pg. 170-171 30-39 odd, 40-43 all