# Algebra: Solving Basic Equations

## Solving Basic Equations

If algebraic expressions are the logical equivalents of sentence fragments, then equations are the equivalents of full sentences. What's the difference between a phrase and a full sentence? The presence of a verb, and in the case of equations, the mathematical verb will be "equals."

Believe it or not, I think you'll find equations refreshing, especially compared with the stuff from the first few sections. Not only was that review, but it had one major weakness: There was no easy way to tell if you got a given problem right! Sure, if asked to divide two fractions, you can probably remember to take a reciprocal and multiply, but if you make an arithmetic mistake, you're doomed! You might have had the right idea, and knew what you were supposed to do, but because of a simple screwup (like multiplying 3 by 7 and getting 10), your test paper will be covered in so much red ink that it will look like it was attacked by a badger.

That's not true for equations. When you finish solving an equation, you can test your answer, and instantly find out if you were right or not. If something went wrong, you can go back and fix it before it gets marked wrong, leaving the badger to do nothing but make whatever sounds badgers make when they're frustrated.

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.