Worked example: two-step equations

We have the equation negative 16 is equal to x over 4, plus 2. And we need to solve for x. So we really just need to isolate the x variable on one side of this equation, and the best way to do that is first to isolate it-- isolate this whole x over 4 term from all of the other terms. So in order to do that, let's get rid of this 2. And the best way to get rid of that 2 is to subtract it. But if we want to subtract it from the right-hand side, we also have to subtract it from the left-hand side, because this is an equation. If this is equal to that, anything we do to that, we also have to do to this. So let's subtract 2 from both sides. So you subtract 2 from the right, subtract 2 from the left, and we get, on the left-hand side, negative 16 minus 2 is negative 18. And then that is equal to x over 4. And then we have positive 2 minus 2, which is just going to be 0, so we don't even have to write that. I could write just a plus 0, but I think that's a little unnecessary. And so we have negative 18 is equal to x over 4. And our whole goal here is to isolate the x, to solve for the x. And the best way we can do that, if we have x over 4 here, if we multiply that by 4, we're just going to have an x. So we can multiply that by 4, but once again, this is an equation. Anything you do to the right-hand side, you have to do to the left-hand side, and vice versa. So if we multiply the right-hand side by 4, we also have to multiply the left-hand side by 4. So we get 4 times negative 18 is equal to x over 4, times 4. The x over 4 times 4, that cancels out. You divide something by 4 and multiply by 4, you're just going to be left with an x. And on the other side, 4 times negative 18. Let's see, that's 40. Well, let's just write it out. So 18 times 4. If we were to multiply 18 times 4, 4 times 8 is 32. 4 times 1 is 4, plus 1 is 72. But this is negative 18 times 4, so it's negative 72. So x is equal to negative 72. And if we want to check it, we can just substitute it back into that original equation. So let's do that. Let's substitute this into the original equation. So the original equation was negative 16 is equal to-- instead of writing x, I'm going to write negative 72-- is equal to negative 72 over 4 plus 2. Let's see if this is actually true. So this right-hand side simplifies to negative 72 divided by 4. We already know that that is negative 18. So this is equal to negative 18 plus 2. This is what the equation becomes. And then the right-hand side, negative 18 plus 2, that's negative 16. So it all comes out true. This right-hand side, when x is equal to negative 72, does indeed equal negative 16.