Q&A #9409

Solving algebraic equations

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From: Suzanne A. (for Teacher2Teacher Service)
Date: Sep 22, 2002 at 10:33:26
Subject: Re: Solving algebraic equations

Hi Lisa,

Both of these examples could benefit from looking at ways to solve basic 
algebraic equations. When I worked with 7th graders and algebraic thinking I 
always liked to use the example of a scale or a balance. If we use your second 
example first:

    8m + 13 = 13 + 8m

I would ask students to tell me what's on each side of the equals sign. Then I 
would ask them what happens if m equals 0? Is the equation true? Then I'd have 
some other numbers until they had convinced themselves that no matter what 
number they use for m, the equation is always true.

The second example:

    4x - 9 = 7x + 12

We could try the same technique again. Let x equal 0. Is the equation true? 
No, it's not because -9 does not equal 12. Now using some techniques to solve 
basic equations can be helpful. If we remember that the equals sign is the 
middle of the teeter-totter or balance, we know that whatever we do to one 
side, we can do to the other. Let's start by adding 9 to both sides.

    4x - 9 + 9 = 7x + 12 + 9

(I would ask students to suggest something, actually, and they may suggest 
something different...but that's okay. With time they'll "see" what they do 
first might save them some time.)

    4x = 7x + 21

What happens if we subtract 7x from both sides?

    4x - 7x = 7x - 7x + 21

Now I have,

       -3x = 21

If I divide both sides by -3, I get

        x = -7

NOW, let's check to see if that works. I go back to my equation, 4x - 9 = 7x + 
12 and instead of x I write (-7):

     4(-7) - 9 = 7(-7) + 12

and doing the arithmetic, I have:

    -28 - 9 = -49 + 12
    -37 = -37

It worked! I hope that gives you some ideas.

 -Suzanne A., for the T2T service

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