Overview
On this page, we discuss inequalities involving an absolute value and how to solve them.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Graph the solution of an inequality where \(|x|\) has already been isolated, and interpret such an inequality as a statement about the distance between \(x\) and zero.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Solve an inequality involving an absolute value by isolating the absolute value, then rewriting the result as a compound linear inequality.
To prepare for class
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Watch the following video (by Tyler Wallace) which shows how to graph the solution to an inequality where \(|x|\) has already been isolated, and write it in interval notation:
After class
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Watch the following videos (by Tyler Wallace) which show examples of solving inequalities with absolute values by isolating the absolute value then rewriting the result as a compound inequality: