And so what we're going to be left with is x and then the sevens cancel out is equal to ten minus seven is equal to three. I want to subtract seven from the left-hand side, but if I want to maintain an equality here, whatever I do to the left-hand side I also have to do to the right-hand side going back to our scales that's so that we can keep our scale balanced, so that we can say that the left is still equal to the right.

Well if all I want on the left hand side is an x I'd want to get rid of the seven.

All its saying is something plus seven is equal to ten, and you might be able to figure that out in your head, but if you want to do it a little bit more systematically, you're like well just all I want on the left hand side is an x. So let's say that you have x plus seven is equal to ten, and I want to solve for x. Now that we're comfortable with the 'why' of why we do something to both sides of an equation, let's see if we can apply it to some equations to solve for an unknown variable.

Khan academy equations