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### Solving Single Variable Equations

```
Date: 02/02/97 at 13:36:50
From: JAMSHID FOROUSHANI
Subject: Two-step equations

How do you do two-step equations?

One problem is 4g + 7 = 35.  I don't understand it and the math book
says to do this to solve it:

No. 1  Undo addition or subtraction
No. 2  Undo multiplication or division

My teacher explained it to us but she just said "Okay, now here's how
to do it...." Then all she did was solve the problem.

Susie Foroushani
```

```
Date: 02/02/97 at 21:15:13
From: Doctor Steven
Subject: Re: Two-step equations

Hi Susie!

We'll solve the equation: 4g + 7 = 35

First you subtract 7 from both sides of the equation (undoing the
addition): 4g + 7 - 7 = 35 - 7

Simplify: 4g = 28.

Then you divide by 4 (undoing the multiplication): 4g/4 = 28/4

Simplify: g = 7

You're done.

Hope this helps.

-Doctor Steven,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 02/02/97 at 22:11:14
From: JAMSHID FOROUSHANI
Subject: Re: Two-step equations

Thanks so much!  Now I understand everything except for one part. How
did you subtract 7-7?  Thanks for the help.

Greatfully yours,
Susie
```

```
Date: 02/02/97 at 22:52:31
From: Doctor Mike
Subject: Re: Two-step equations

Hi Susie,

I read Dr. Steven's message to you.  This is a very important math
technique which is tricky to understand fully. But, when you do
understand it, it is really powerful.  I am glad to give you another
explanation of it, and I think if you will compare what you heard from
your teacher, and what you heard from both of us, it will be clear.
Here goes:

The problem you sent, "4g + 7 = 35", is an equation.  You know that
already, but I want to emphasize it, because it is very important for
you to keep in mind that both sides of it (left and right) are EQUAL.
They are the same thing, just expressed in different ways.

You said what still is a puzzle is that first step, so I will
concentrate on that.  What Dr. Steven was doing was subtracting 7 from
both sides of the equation. You can do that because (remember) the
left and right parts are the same. If you start out with 2 things that
are identical, and you do exactly the same to both of those things,
then the results are the same. Both sides of the equation are the
same. That's given; it's a guaranteed thing.  So if you subtract seven
from both sides, then the new left side is going to be equal to the
new right side.  You have another new true equation.  Let's do that
now.

When you subtract 7 from the right side you are doing 35-7 which is
28. That's easy. When you subtract 7 from the left side you have to
be just a little more sophisticated. Saying (4g+7)-7 means that you
are multiplying the unknown amount "g" by 4, then adding 7 to it, and
THEN subtracting seven. If you add 7 and then take away seven the
result is zero, right?  That's what is going on here. When Dr. Steven
said to simplify 4g+7-7 to get 4g, that's what he meant. We do not
know what g is yet, but whatever g is, 4g is some number. And if you
add 7 to 4g and then turn right around and subtract 7 you haven't
really changed anything permanently. It's still just 4g.

Here is another way to write down problems like this. You no doubt
are familiar with doing addition and subtraction problems by putting
one over the other and the + or - sign on the second line to the left
of the second number. Like this:

468
-123
------
345

You can do the same thing when you have a step that involves adding or
subtracting the same thing with both sides:

4g + 7 = 35
-7   -7
-------- ----
4g     = 28

You can do the same thing in the next step for dividing both sides by
4, but I can't show that because my keyboard doesn't have that special
symbol for division (horizontal line with a dot above it and a dot
below it).

Keep trying to understand the new ideas your teacher presents in
class, and you will do fine. If you get into a rough spot again,
then just write back to us.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 02/03/97 at 18:20:25
From: JAMSHID FOROUSHANI
Subject: Re: Two-step equations

Thank you you much!  I really understand now!  THANK YOU!

Susie
```
Associated Topics:
Middle School Algebra

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