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Now that we're comfortable with the "why" of why we do something to both sides of an equation,

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let's see if we can apply it to some equations to solve for

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an unknown variable. So let's say that you have x plus seven is equal to ten, and I want to solve for x.

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All its saying is something plus seven is equal to ten, and you might be able to figure that out in your head,

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but if you want to do it a little bit more systematically, you're like well just

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all I want on the left hand side is an x. Well if all I want on the left hand side is an x

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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

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here, whatever I do to the left-hand side I also have to do to the right-hand side going back to our scales

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that's so that we can keep our scale balanced, so that we can say that the left is still equal to the right.

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And so what we're going to be left with is x and then the sevens cancel out

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is equal to ten minus seven is equal to three. So that unknown is three,

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and you can verify it, three plus seven is indeed equal to ten.

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Let's try one more. Let's say we have a minus five is equal to negative two.

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So this is a little bit more interesting since we have all of these negative numbers here, but we can use

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the exact same logic. We just want an a over here on the left-hand side

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so we have to get rid of this negative five somehow.

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Well the best way of getting rid of a negative 5 is to add five to it.

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So I'll do that. So I will add five to the left-hand side.

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But if I want the left-hand side to stay equal to the right-hand side,

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whatever I do to the left I have to do the right.

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So I'm going to have to add five on the right-hand side as well,

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and so on the left-hand side I'm left with a, and then the negative five and the positive five cancel out

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and on the right hand side, and they're going to stay equal because I did the same thing to both sides,

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we have negative two plus five which is equal to three.

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So a is equal to three. Once again you can verify it.

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Three minus five is indeed equal to negative two.