Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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

Terms you should be able to 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 nn, union uu

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.

Mini-Lectures and Examples

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"

rev. 2020-10-10