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