Writing Out Equations

Date: 12/18/97 at 16:20:21
From: Danielle
Subject: Math: Equations....ex: 6x+7=3x+16

6x+7 = 3x+16

Here's how I tried it:

I subtracted 3x from 6x and 3x and I got 3x+7 = 10.

I don't know if this is right, but I am stuck at this point.

Date: 01/05/98 at 12:35:24
From: Doctor Otavia
Subject: Re: Math: Equations....ex: 6x+7=3x+16

Hi! I myself often mess this sort of thing up, by forgetting a term or 
something like that, so I find it easiest to do this kind of problem 
if I write everything out. So let's take your problem and see how we 
would write everything out.  

We start with the equation.

   6x + 7 = 3x + 16

You were on the right track with subtracting 3x. But when you say you 
are subtracting 3x from 6x, what you're really doing is subtracting 3x 
from both sides, so you write

   6x + 7 - 3x = 3x + 16 - 3x .

You then combine like terms, and get

   6x - 3x + 7 = 3x - 3x + 16.
   3x + 7      = 0 + 16.
   3x + 7      = 16.

So, now we want to solve for x, right? That means that we want x to be 
alone on one side of the equals sign, so we subtract 7 from both sides 
to get x alone.

    3x + 7 - 7 = 16 - 7.

Now we combine like terms.

        3x + 0 = 9
            3x = 9

Now all that's left to do is divide both sides by the coefficient of 
x, so we get something that looks like x = .....  In this case, we 
divide both sides by 3, (which is really the same as multiplying by 
1/3) and get

   (1/3)*3x = (1/3)*9
          x = 3

So there we have an answer for x! The trick with this kind of problem 
is to write every step down so you don't miss anything or add 
incorrectly. After you become more comfortable with this kind of 
problem, you can write fewer things down, but when starting out, it 
makes things much easier.  

I hope this helps, and good luck!

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