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## Manipulating expressions with unknown variables

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# Manipulating expressions using structure (example 2)

CCSS.Math:

## Video transcript

- [Voiceover] We're told, suppose a+b=2a. Which of these expressions equals b-a? Alright, I encourage
you to pause the video and see if you can figure that out. Which of these expressions would be equal to b-a and it's going to just involve
some algebraic manipulation. Alright, let's work through this together. So we are told, we are told that a+b=2a so the first thing I would want to do is get all my a's in one place and one way I could do that is I could subract a from both sides. So if I subtract a from both sides I'm going to be left with
just a b on the left-hand side and on the right-hand side
I'm going to be left with 2a-a, well that's just going to be a. If I have two of something
and I subtract one of them, take away one of them I'm going to have just one of those somethings equal to 1a. So we want to figure out what b-a is. Well luckily I can figure that out if I subtract a from both sides. So if I subtract a from both sides well then I'm going to
get on the left-hand side b-a, which is what we want to figure out, is equal to a-a=0. So b-a=0 which is not one of the choices. Alright, so let's see if we can figure out some other things over here. So b-a=0 but that is
not one of the choices. Alright, so let's see is there any other way to manipulate this? No, b minu- I could just go straight ahead and subtract 2a from both sides and I would get b-a=0. Oh, this is interesting,
this is a tricky one. So b-a=0. Well, if b-a=0 then if we take the negative of both sides of this, if we take the negative of both sides, if we multiply both sides by -1. So x, I should write the times,
I should write like this, alright, because we don't want to confuse it with the variable x, so if we multiply both sides by -1 what do we get? Well on the left-hand side we get a-b and on the right-hand side we still get 0. If b-a=0 then the negative of it, which is a-b is also
going to be equal to 0. And that's this choice. That is, let me do that
in a little darker color, that is this choice right over there. That was a good one.