# Separated Variables

#### 2unique

##### New member
I have this problem.
7c-3c=c+27
I know that you combine like terms.
so
7c-3c=4c
but I a unsure of what to do with the rest. I also know that any variable by itself is to be considered 1.
So where do i go from here?
Thanks #### tkhunny

##### Moderator
Staff member
What is the point of combining terms? It should do something for you.

7c - 3c = c + 27

Combine the left side.

4c = c + 27

Use subtraction to get the other straggler.

4c - c = c - c + 27

Simplify

3c = 0 + 27 = 27

Now what?

J

#### JeffM

##### Guest
2unique said:
I have this problem.
7c-3c=c+27
I know that you combine like terms.
so
7c-3c=4c OK That simplifies the left hand side of the equation. Very good. It would help (particularly me, who am getting old) to write out what the problem equation is now that you have simplified. Like this: 7c - 3c = 4c = c + 27.

but I a unsure of what to do with the rest. [Meaning the right hand side of the equation, silly me for not understanding before.]
I also know that any variable by itself is to be considered 1. Correct you are.

So where do i go from here? Eventually to get that GED I hope. Can you simplify 4c? No. Can you simplify c or 1c? No. You have an equation with fully simplified expressions containing the unknown on BOTH sides of the equation. They are SEPARATED by the equal sign. So, the only way to simplify further is first to get all the references to the unknown on the same side of the equal sign and then simplify some more. That is the general trick in solving for an equation in a single unknown: you get a simplified expression involving only the unknown on one side of the equation and a single number on the other side of the equation.

#### mmm4444bot

##### Super Moderator
Staff member
2unique said:
I also know that the coefficient on any variable by itself is to be considered 1. J

#### JeffM

##### Guest
Re:

mmm4444bot said:
2unique said:
I also know that the coefficient on any variable by itself is to be considered 1. Thanks mmm4444bot. I think a few synapses went haywire. I completely misread the original post. I have corrected my response.