Algebra: Linear Inequalities

Linear Inequalities

When Thomas Jefferson wrote that "all men are created equal" in the Declaration of Independence, he probably meant it in a philosophical and political way. That is to say, all people should have the same rights and responsibilities as citizens of a country. Practically speaking, it would be hard to argue that all men (and women) are actually created equal. If that were true, it wouldn't make much difference if the coach of the St. Louis Rams decided to let me play quarterback during the playoffs.

If all men were created equal, I would possess immeasurable athletic talent, and could throw a 60-yard pass that resulted in the winning touchdown, to the praise and glory of thousands of fans, who would chant my name and buy my bobble-head dolls at the concession stand. In real life, if I were in for a single play, we both know what would happen. I'd get sacked by the meanest 350-pound defensive linemen you've ever seen, instantly breaking every major bone in my body, and single-handedly destroying any chance that my face would ever be attached to any toy, whether its head bobbled or not. (Unfortunately, my real head would probably bobble permanently from that point on, though the effect is less comical in real life, I assure you.)

In any case, people are rarely created exactly equal, and so, too, mathematical statements are often unequal. In this section, I'll describe algebraic sentences, called inequalities, that aren't equations because their sides are unequal. The good news is that solving such statements involves a process nearly identical to solving equations. The only major difference you'll find is that the graphs of inequalities are a bit different than the graphs of equations.

Excerpted from The Complete Idiot's Guide to Algebra © 2004 by W. Michael Kelley. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.

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