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Why we do the same thing to both sides of equations | Linear equations | Algebra I | Khan Academy with English subtitles  
  

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.

And we also have a bunch of 1 kilogram masses.

These are all each a 1kg 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?

I will give you a couple of seconds to think about it.

To figure out what this mystery mass is,

we essentially just want this on one side of this scale

But that by itself is not enough.

We could just remove these three,

but that won't do the job, because

if we just remove these three,

then the left side of this scale

is clearly going to have less mass,

and it will go up, and the right side will go down.

And that will not give us much information.

It would just tell us that this blue thing

has a lower mass than what is over here.

So just removing this will not help us much.

I won't let us know that this is equal to that.

What we have to do if we want to keep the scale balanced,

is that we have to remove the same amount of mass

from both sides of the scale.

So, if we want to remove 3 things here,

(let me try my best to remove 3 things here)

(I will just erase it)

If we want to remove 3 things there,

If we did this by itself,

just removed these 3 things,

the two sides would not have an equal mass anymore.

this side would have a lower mass.

So we have to remove 3 from both sides.

If we want to make sure our scale is balanced,

we have to remove 3 from both sides.

If we started off with the scales balanced,

and then we removed 3 from both sides,

the scale will still be balanced

and then we would have a clear idea

of what the mass of this object actually is.

Now, with 3 removed from both sides,

the scale will still be balanced,

and we know that this mass

is equal to whatever is left over here.

It is equal to 1, 2, 3, 4, 5, 6, 7

- and if we're assuming they are kilograms -

we'll know that the question mark mass

question mark is equal to 7 kilograms.

So this is a seven kilogram mass.

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