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