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Solving Single Variable Equations

Date: 02/02/97 at 13:36:50
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!   

Date: 02/02/97 at 22:11:14
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,

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 
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: 
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!   

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

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

Associated Topics:
Middle School Algebra

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