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### Algebra - Solving Equations

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Date: 11/03/97 at 23:36:50
From: AVI MANTHA
Subject: ALGEBRA

Hi, Dr. Math,

I am in an enriched Algebra class, and I'm having a hard time solving

4 - 3X = 5 - 6X - 7

7X = 5(X - 12)

Please explain the solution step by step.

Thank you very much for your help.
Avi
```

```
Date: 11/10/97 at 09:28:19
From: Doctor Allan
Subject: Re: ALGEBRA

Hello Avi, and thanks for writing to Dr. Math!

You do not tell me exactly where you have problems, so I am not sure
whether you have problems with these types of equations generally, or
if it is just the two problems you mention here.

What I will do is give you techniques to use when solving these
you can check out whether that helps you solving the second problem
and getting the general picture.

When you want to solve an equation you want to find values such that
if you substitute these values for x in your equation, you will get
something that is true. Let me give you an example:

x + 5 = 8

What you need to do is find a value to substitute for x such that you
get 8. If you have five apples and you want to have eight apples how
many more apples should you buy?

That's basically what an equation is all about.

So the smart thing to do is to isolate x on one side of the equation
and that will tell you the exact value to be substituted.

In order to do this you have to remember some rules. The most
important one is this:

Whatever you do to one side of the equation you should do to
the other side.

That means if you for instance add 3x to one side you should add 3x to
the other side.

Furthermore, there is the distributive rule:

x(a+b) = (a+b)x = xa+xb

This means that when you multiply terms within a parenthesis by x, you
multiply x by each term of the parenthesis.

That should cover the basics. Now let's go to the first of your
problems:

4 - 3x = 5 -6x -7

First notice that 5 - 7 = -2 so you get

4 - 3x = -2 -6x

Now you want to isolate x on one side of the equation, so let's
subtract 4 from each side of the equation. We get

4 - 3x - 4 = -2 - 6x -4

That is

-3x = -6 -6x

Since you want the x on one side the thing to do now is to add 6x:

-3x + 6x = -6 - 6x + 6x

That is

3x = -6

So all you need to do now to isolate x is to divide by 3 on each side:

(3x)/3 = (-6)/3

So you get

x = -2

I hope this helped you. If you have further questions, please write

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

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