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Course: College Algebra
Topic: Equations and Inequalities
Subtopic: Compound and Absolute Value Inequalities

Overview

Before covering compound inequalities (the "and" intersection kind, the "or" union kind, the "double" inequality kind) you may benefit by reviewing linear inequalities from an elementary algebra course. The reason being that, for instance, |x-2|=3 means x-2=3 OR x-2=-3. Similarly |x-2|<3 means -3<x-2<3 and |x-2|>3 means x-2<-3 OR x-2>3. Do you see that the absolute value inequalities reduce to double or union type compound inequalities?

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 1.2.1 Write sets using interval notation, inequality notation, or set-builder notation, and graph sets on a number line using open or closed circles appropriately
• 1.2.2 Understand the union or intersection of two sets
• 1.2.3 Algebraically solve compound inequalities of all three types: "and", "or", and double
• 1.2.4 Solve compound inequalities graphically
• 1.2.5 Solve absolute value inequalities algebraically and graphically

Terminology

Define: set, solution set, number line, inequality sign, inequality notation, set-builder notation, interval notation, open interval, closed interval, clopen interval, linear inequality in one variable, compound inequality, double inequality, intersection ∩, union ∪

Text Notes

Review set notation from elementary algebra: interval notation vs. inequality notation vs. graphing solutions on a number line. Interval notation is the notation most commonly used to express answers to inequalities in calculus.

When writing the final answer to a compound inequality be sure to condense it down to a single interval where possible. Pay particular attention to this with the "or" and "and" kinds.

Practice solving inequalities graphically as well as algebraically.

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics:
"Using Interval Notation"
"Solving and Graphing Compound Inequalities"
"Solving Absolute Value Equations"
"Solving Absolute Value Inequalities"