Equations with Variables
Date: 9/23/96 at 19:34:48 From: daugherty Subject: Variables on Both Sides Dr. Math, How do you solve problems with variables on both sides? Here's one I'm working on: 6 - 2y = 7y + 13 I just can't figure it out! Would you please walk me through it and explain WHY you're doing things? Thanks a million! Rachel Daugherty
Date: 10/18/96 at 17:49:6 From: Doctor Lynn Subject: Re: Variables on Both Sides Hello, Rachel. This kind of problem isn't too difficult once you get the knack of it. What you need to do is to get rid of one of the variables from one side. In your equation, 6 - 2y = 7y + 13 you can either get rid of the -2y or the 7y, but it's generally easier if you get rid of the negatives, so I'll show how to get rid of the 2y. The most important rule for equations is that you always do the same thing to both sides of the equation. Now, to get rid of the -2y we need to find what operation we can do to the lefthand side of the equation so that the -2y becomes zero. Well, the opposite of a negative is a positive, so we add 2y to the lefthand side of the equation. We must also do the same to the righthand side, like this: 6 - 2y + 2y = 7y + 13 +2y The equality sign "=" means that both sides of the equation are exactly the same. We have done the same thing to both sides, so the two sides are still the same. But now on the lefthand side, we have -2y+2y, which is clearly zero. This means that we can rewrite the equation without these terms: 6 = 9y + 13 We now cancel the +13 in the same way, so that the numbers and variables are on separate sides of the "=": 6 = 9y + 13 6 - 13 = 9y + 13 - 13 -7 = 9y Finally, we will cancel the implied multiplication by 9 by dividing both sides by 9: -7/9 = y So in summary, the points to remember are: Every operation has an opposite. To "get rid of a term", you simply apply the opposite operation to both sides. You are trying to get the numbers on one side of the "=" and the variables on the other. I hope that helps. Write back if you have any more problems. -Doctor Lynn, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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