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### Multiple Step Equations

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Date: Wed, 7 Dec 1994 16:31:42 -0800 (PST)
From: Phong Huynh
Subject: Math Probs

I am having problems with math problems like:

29 + q = -2(q - 13)
and     -2(c + 7) - 30 = 9c

These are multiple step equations that I am having problems with.
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Date: Wed, 7 Dec 1994 19:58:16 -0500 (EST)
From: Dr. Sydney
Subject: Re: Math Probs

Hello there!  Thanks for writing Dr. Math!  We'd love to help you with
your math problems.  These can get a little tricky because it seems like
there are lots of steps involved, but if we take it one step at a time,
I think we can make sense of it.

Okay, you are given an equation with an unknown, and you are asked to
solve for the unknown.  The general approach to problems like this is to
get all the terms with the unknown on one side of the equals sign with the
constants on the other side of the equals sign.  Then you work with the
equation until you have only the unknown on one side of the equals sign.

Let's look at your problems, and try this strategy:

First, what is q if 29 + q = -2(q - 13)?

Our first step is to get all the terms with q's on one side of the equals
sign with constants on the other side.  But before we can do that, we have
to simplify the right hand side of the equation.  We need to distribute the
-2.  So simplifying the right hand side of the equation, we get:

-2(q - 13) = -2q + 26

So, the equation becomes:

29 + q = -2q + 26

Now, we want all the terms that have a q in them on one side of the equals
sign and all the constants on the other side.  So, let's add 2q to both
sides and subtract 29 from both sides.  Then we have:

2q - 29 +  29 + q = -2q + 26 + 2q - 29

This reduces to:

3q = -3

Now we are almost done.  We want to know what q is, so if we divide both
sides of the equation by 3, we will get our answer:

3q/3 = -3/3

So, we have:

q = -1

You can always check your answer by plugging in -1 to the original
equation.  So, check:  is 29 - 1 equal to -2( -1 - 13)?  Yes, it is, so we
did everything right.

Did that make sense to you?  I guess the steps you should take are:

1) Simplify (distribute if necessary)
2) Put like terms with like terms (Put all the terms containing the unknown
on one side of the equals sign with the constants on the other side)
3) Divide or do what you must to simplify

I hope this helps.  Maybe you could do the second example and write back

--Sydney
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Associated Topics:
Middle School Equations

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