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: Elementary Algebra
Topic: Linear Equations and Inequalities
Subtopic: Solving Compound Inequalities

Overview

Compound inequalities means to combine two or more inequalities together. There are three ways to do this.

• Two inequalities can be connected by an "and" (intersection) which means that the final answer will be those numbers that are in both sets (the overlapping region).
• Two inequalities can be connected by an "or" (union) which means that the final answer will be those numbers that are in one set or the other or both -- basically the answer will be both sets all lumped together.
• The third way to compound inequalities is the "double inequality" kind covered in the previous lesson notes.
The final answers to these compound inequalities will usually be written in interval notation, but could be given in interval notation or graphed on a number line.

Treat this section as an introduction to compound inequalities. This topic will be covered more thoroughly in a college-level course.

Objectives

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

• 2.7 1 Combine solution sets connected by "and", "or" algebraically
• 2.7.2 Combine solution sets connected by "and", "or" graphically on a number line
• 2.7.3 Recognize no solution and all solution cases from an "and" or "or" compound inequality
• 2.7.4 Solve "and" and "or" compound linear inequalities correctly

Terminology

Terms you should be able to define: compound linear inequality, intersection ∩, union ∪

Text Notes

Many textbooks cover business applications of inequalities at this time. If yours does you can SKIP the business applications, revenue function, cost function, profit function, and all of the graphing stuff! You will NOT be tested on these topics in this level course.

If your textbook covers equations/inequalities that contain absolute values you may SKIP these problems! You will NOT be tested on these topics in this level course.