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## Linear equations with variables on both sides

Current time:0:00Total duration:4:06

## Video transcript

We have the equation 20 minus
7 times x is equal to 6 times x minus 6. And we need to solve for x. So the way I like to do these
is we just like to separate the constant terms, which are
the 20 and the negative 6 on one side of the equation. I'll put them on the
right-hand side. And then we'll put all the x
terms, the negative 7x and the 6x, we'll put it all on
the left-hand side. So to get the 20 out of the way
from the left-hand side, let's subtract it. Let's subtract it from
the left-hand side. But this is an equation,
anything you do to the left-hand side, you also have to
do to the right-hand side. If that is equal to that, in
order for them to still be equal, anything I do to the
left-hand side I have to do to the right-hand side. So I subtracted 20 from the
left, let me also subtract 20 from the right. And so the left-hand side
of the equation, 20 minus 20 is just 0. That was the whole point,
they cancel out. Don't have to write it down. And then I have a negative 7x,
it just gets carried down. And then that is equal to the right-hand side of the equation. I have a 6x. I'm not adding or subtracting
anything to that. But then I have a negative
6 minus 20. So if I'm already 6 below 0 on
the number line, and I go another 20 below that, that's
at negative 26. Now, the next thing we want to
do is we want to get all the x terms on the left-hand side. So we don't want this 6x here,
so maybe we subtract 6x from both sides. So let's subtract 6x from the
right, subtract 6x from the left, and what do we get? The left-hand side, negative
7x minus 6x, that's negative 13x. Right? Negative 7 of something minus
another 6 of that something is going to be negative 13
of that something. And that is going to be
equal to 6x minus 6x. That cancels out. That was the whole point by
subtracting negative 6x. And then we have just a negative
26, or minus 26, depending on how you want to
view it, so negative 13x is equal to negative 26. Now, our whole goal, just to
remember, is to isolate the x. We have a negative 13
times the x here. So the best way to isolate it is
if we have something times x, if we divide by
that something, we'll isolate the x. So let's divide by
negative 13. Now, you know by now, anything
you do to the left-hand side of an equation, you have to
do to the right-hand side. So we're going to have to
divide both sides of the equation by negative 13. Now, what does the left-hand
side become? Negative 13 times x divided
by negative 13, that's just going to be x. You multiply something times x,
divide it by the something, you're just going to
be left with an x. So the left-hand side
just becomes an x. x is equal to negative 26
divided by negative 13. Well, that's just positive
2, right? A negative divided by a negative
is a positive. 26 divided by 13 is 2. And that is our answer. That is our answer. Now let's verify that
it really works. That's the fun thing
about algebra. You can always make sure that
you got the right answer. So let's substitute it back into
the original equation. So we have 20 minus 7 times x--
x is 2-- minus 7 times 2 is equal to 6 times x--
we've solved for x, it is 2-- minus 6. So let's verify that this
left-hand side really does equal this right-hand side. So the left-hand side simplifies
to 20 minus 7 times 2, which is 14. 20 minus 14 is 6. That's what the left-hand
side simplifies to. The right-hand side, we have 6
times 2, which is 12 minus 6. 12 minus 6 is 6. So they are, indeed, equal, and
we did, indeed, get the right answer.