The division rule for equations states that if you divide both sides of an equation by the same number, then you’re not changing the equation. So if you take two x is equal to eight, remember, anytime you have a number beside a variable, it implies multiplication, so it is two times x equals eight. So I am going to divide each side of the equation by two. Remember, when I use a fraction bar it means divide, so don’t get too concerned by the fraction bar. This just means two x divided by two, and the twos cancel each other out because two divided by two equals one, and you can drop the coefficient of one because it is implied, so I get x. And let’s look at eight divided by two or eight over two; eight divided by two is four. So now I can check to make sure that I am right by multiplying two times four and checking to make sure that equals eight, and it’s correct. So four is the correct solution to the equation two x equals eight.

Let’s try this one—twelve equals four times c. This time the variable is on the righthand side, which is fine. You can swap these if you want; if you’re more comfortable, you can rewrite this as four c equals twelve, or you can leave it in its original form. I’m going to divide both sides of the equation by four, and I’m left with c equals twelve divided by four, or three.