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## Algebra I (2018 edition)

### Unit 2: Lesson 2

Why we do the same thing to both sides of an equation# Same thing to both sides of equations

The example of a scale where we try to achieve balance helps to explain why we do the same thing to both sides of an equation. Created by Sal Khan.

## Video transcript

We've got a scale here, and as
you see, the scale is balanced. And we have a
question to answer. We have this mystery
mass over here. It's a big question mark on
this blue mass right over here. And we also have
a bunch of 1-- I guess we could call
them 1-kilogram masses. So these are all each
a 1-kilogram mass. And my question to
you is, what could we do to either side of
this scale in order to figure out what
the mystery mass is? Or maybe we can't
figure it out at all. Is there something that we can
do, either removing or adding these things, so that
we can figure out what this mystery mass is? And I'll give you a couple of
seconds to think about that. Well, to figure out what
this mystery mass is, we essentially just want this
on one side of this scale. But that by itself isn't enough. We could just remove these
3, but that won't do the job, because if we just
remove these 3, then the left-hand
side of the scale is clearly going to have less
mass, and it's going to go up, and the right side
is going to go down. And that's not going to
give as much information. It's just going to tell us that
this blue thing has a lower mass than what's over here. So just removing this
won't help us much. It won't let us know that
this is equal to that. Well, what we've got to do
if we want to keep the scale balanced is we've got to
remove the same amount of mass from both sides of the scale. So if we want to remove
3 things here-- so let me try my best to
remove 3 things here. If we want to remove 3--
let me do it like this. I'll just color on it. I'll just erase it. So if we want to
remove 3 things there, if we did this by itself,
just removed these 3 things, then the two sides would not
have an equal mass anymore. This side over here
would have a lower mass. So we've got to remove
3 from both sides. So if we really
want to make sure that our scale is
balanced, we've got to remove 3 from both sides. And so if we started off
with the scales balanced and then we removed
3 from both sides, the scale will
still be balanced. And then when we do that,
we have a clearer idea of what the mass of
this object actually is. Now, when we remove
3 from both sides, the scale will
still be balanced. And we know that this mass
is equal to whatever's left over here. It's equal to 1,
2, 3, 4, 5, 6, 7. And if we're assuming
they're kilograms, we'll know that
the question mark mass is equal to 7 kilograms,
that this right over here is a 7-kilogram mass.