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# Representing a relationship with an equation

Equations are about relationships (no, not girlfriends and boyfriends!) between the two sides of the equation. Let's again use a scale example to help us understand. Created by Sal Khan.

Video transcript

I now want to refigure out
what this mystery mass is, but we're going to start using a
little bit more of mathematics. And mathematics really
are just a language, symbols for representing ideas,
for representing relationships between things. And so the first
thing I want you to do is think about if you can
express a relationship mathematically between
this side of the scale and that side of the scale. And I'll give you some hints. We know that they
have equal mass. So maybe you can
set up some type of relationship using an
equal sign, somehow showing that this right over
here is equal to that. And I'll give you a
few seconds to do that. So let's think about
it a little bit. What do we have on this side? Well, we have our mystery mass. And I'll represent
that mystery mass by the question mark
right over here. But that's not the
only thing that we have on the left-hand side. We also have these
other 3 kilograms. So let me write over here. We'll assume that we're
dealing with kilograms. So we have the mystery
mass in kilograms plus 3 more kilograms. That's what we have here
on the left-hand side. Now, what do we have here
on the right-hand side? Well, we just have 1, 2, 3, 4,
5, 6, 7, 8, 9, 10 kilograms. So we just have 10. We just have 10 on
the right-hand side. And what else do we know? Well, we know that this scale
is balanced, that the mass here is equal to the mass here. Because the scale is balanced
the way it's been drawn, we know that these
two things are equal. So we have just
set up an equation. We're using question
mark as our unknown. We don't know what
this mystery mass is. If we add 3 kilograms
to it, then we see that it has the exact
same mass as 10 kilograms. Now my question to you is,
what can we do to this equation so that we can essentially
solve for the unknown, so that we can figure
out what the unknown is? Well, we saw in the
last little problem that we had that if we wanted
to figure out this mystery mass, we had to remove 3
kilograms from both sides. If we just removed 3
kilograms from one side, then the scale wouldn't
be balanced anymore. And we really wouldn't be able
to say that the mystery mass is equal to the thing on the right. In order to say they're
equal, the stuff has to actually be balanced. So in the last video,
we removed 3 of these. We removed 3 kilograms
from both sides in order to keep
the scale balanced. So mathematically, we'll do
the exact same thing over here. We will remove 3,
not from one side. If we remove 3 from
one side, then it wouldn't be equal anymore. We need to remove
3 from both sides. So we need to remove 3. We need to subtract 3 from
both sides of this equation in order to keep
the scale balanced. So on the left-hand side,
what are we left with? Well, just like over here, we're
left with just the question mark. 3 minus 3 is 0. So on the left-hand side, we're
left with just the question mark. And on the right-hand side,
we're left with 10 minus 3, which is 7. And we get the
exact same result. Question mark is equal to 7. And if we're dealing
with kilograms, then this is 7 kilograms.