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### Isolate the Variable

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Date: 9/9/96 at 16:21:50
From: Anonymous
Subject: Simplifying Equations of Numbers, Variables

Dear Dr. Math

What are the steps needed to solve:

4c + 23 = 9c - 7
```

```
Date: 9/9/96 at 22:12:3
From: Doctor Ana
Subject: Re: Simplifying Equations of Numbers, Variables

I'm going to solve a different problem to show you how to solve this
type of problem.

There is only one big thing to remember, and that is to ISOLATE the
variable.

5x - 17 = -x + 7

The first step to isolating the variable is to get any term with the
variable in it on one side of the equation. To do this, we are going
to add x to both sides of the equation.

5x - 17 + x = -x + x +  7

This simplifies to

6x - 17 = 7

The next step is to get rid of everything else that is on the same
side of the equation as the variable.  To do this, we will add 17 to
both sides of the equation.

6x - 17 + 17 = 7 + 17

This simplifies to

6x = 24

Finally, the only thing left with the variable is the coefficient
of 6. To completely isolate the variable, we have to divide both
sides of the equation by 6.

x = 24 / 6
x = 4

Now, x is all by itself or "isolated". We can read the answer right
from the equation. x equals 4.

To review, isolating the variable means getting every term containing
the variable on one side of the equation. Then, get any term that
doesn't contain the variable on the other side of the equation.
Finally, combine any terms that aren't already combined, and get rid
of the coefficient of the variable, if there is one.

-Doctor Ana,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra

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