One-step addition & subtraction equations
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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. So let's say that you have x plus seven is equal to ten, and I want to solve for x. 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. Well if all I want on the left hand side is an x I'd want to get rid of the seven. 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. 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. So that unknown is three, and you can verify it, three plus seven is indeed equal to ten. Let's try one more. Let's say we have a minus five is equal to negative two. So this is a little bit more interesting since we have all of these negative numbers here, but we can use the exact same logic. We just want an a over here on the left-hand side so we have to get rid of this negative five somehow. Well the best way of getting rid of a negative 5 is to add five to it. So I'll do that. So I will add five to the left-hand side. But if I want the left-hand side to stay equal to the right-hand side, whatever I do to the left I have to do the right. So I'm going to have to add five on the right-hand side as well, and so on the left-hand side I'm left with a, and then the negative five and the positive five cancel out and on the right hand side, and they're going to stay equal because I did the same thing to both sides, we have negative two plus five which is equal to three. So a is equal to three. Once again you can verify it. Three minus five is indeed equal to negative two.