Craig, when you are told to solve for a variable, what you are trying to do is get that variable by itself on one side of the equal sign and everything else on the other. We do this by doing the opposite operation.
For example, 5x + 2 = 12. Solve for x.
We need to move anything that doesn't have an x to the other side, and the 2 does not have an x, so we do the opposite of addition and subtract 2. We have to do the same thing to both sides of the equal sign! If we write that all out, we get...
5x + 2 - 2 = 12 - 2
If I add 2 and take it away, I've just added nothing, but we don't write +0. They just cancel out. 12 - 2 = 10, so...
5x = 10
Remember that 5x means 5 times x. What's the opposite of multiplication? Division! We divide both sides by 5.
5x/5 = 10/5
What is 5/5? 1, but we don't write 1x, so we end up with...
x = 2
This is our answer. We have just solved for x.
Hope this helps!
David W.
08/24/15