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# Equations and Inequalities

Algebra may not be naturally pretty, but if we have the right foundation, blush, and lipstick, we can enhance its natural features. Of course, we won't be using literal makeup, since that makes the monitor all smeary.

When solving for a variable, we might wind up with a formula that involves some kind of fraction. When that happens, make sure to give the fraction in reduced form.

### Sample Problem

Solve the equation 4z + 2y = 8 for z.

By rearranging, we find that  This is a correct answer, but it's not as nice as it could be. Time to apply the mascara. Multiply the fraction by  (a "clever form of 1") to find that

Ooh la la! Hey equation—are you a model?

Another way to find the same answer is to divide both sides of the original equation by 2 to get:

2z + y = 4

And then solve for z. Thankfully, we find the same answer either way. No going back to the drawing board for us.