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Course: Algebra I / Elementary Algebra
Topic: Linear Equations and Inequalities
Subtopic: Solving Linear Inequalities

Overview

A linear inequality is like a linear equation except it contains an inequality symbol (<, ≤, >, ≥) rather than an equals sign (=). While linear equations have a single solution (eg. x=-4), linear inequalities can have an infinite number of solutions (eg. x≥1).

The process of solving a linear inequality is identical to solve a linear inequality with one big exception. When solving an inequality, watch the direction of the inequality sign. If you multiply or divide both sides of an inequality by a negative number you must reverse the direction of the inequality. Don't forget this important step!

Objectives

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

• 2.5.1 Solve linear inequalities algebraically
• 2.5.2 When solving an inequality, know when the direction of the inequality sign must reverse and be able to perform this step correctly
• 2.5.3 Understand some basic applications of linear inequalities
• 2.5.4 Recognize when a linear inequality has "no solution" or "all solutions"

Terminology

Define: linear inequality in one variable

Text Notes

When studying your textbook for this lesson here are a few things to watch.

• When you text introduces solving linear inequalities they often mention an addition and a multiplication property. I recommend that you put the "additional property of inequality" in your own words instead of making this so complicated. For instance, "It is OK to add (or subtract) a number to both sides of an inequality." Similarly, the "multiplication property of inequality" could be stated as, "It is OK to multiply (or divide) both sides of an inequality by a positive number, but if you multiply (or divide) both sides by a negative number you must reverse the direction of the inequality." Remembering to reverse the direction of the inequality sign whenever you multiply or divide by a negative number is very important!

• Pay attention to the "no solution" and "all solutions" special cases when solving linear inequalities. Watch the class discussion boards examples.