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Isolate the Variable

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 

   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
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Associated Topics:
Middle School Algebra

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