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# Worked example: two-step equations

Video transcript

We have the equation negative
16 is equal to x over 4, plus 2. And we need to solve for x. So we really just need to
isolate the x variable on one side of this equation, and the
best way to do that is first to isolate it-- isolate this
whole x over 4 term from all of the other terms. So in order
to do that, let's get rid of this 2. And the best way to get rid of
that 2 is to subtract it. But if we want to subtract it
from the right-hand side, we also have to subtract it from
the left-hand side, because this is an equation. If this is equal to that,
anything we do to that, we also have to do to this. So let's subtract 2
from both sides. So you subtract 2 from the
right, subtract 2 from the left, and we get, on the
left-hand side, negative 16 minus 2 is negative 18. And then that is equal
to x over 4. And then we have positive 2
minus 2, which is just going to be 0, so we don't even
have to write that. I could write just a plus 0,
but I think that's a little unnecessary. And so we have negative 18
is equal to x over 4. And our whole goal here is
to isolate the x, to solve for the x. And the best way we can do
that, if we have x over 4 here, if we multiply that
by 4, we're just going to have an x. So we can multiply that
by 4, but once again, this is an equation. Anything you do to the
right-hand side, you have to do to the left-hand side,
and vice versa. So if we multiply the right-hand
side by 4, we also have to multiply the left-hand
side by 4. So we get 4 times negative 18 is
equal to x over 4, times 4. The x over 4 times 4,
that cancels out. You divide something by 4 and
multiply by 4, you're just going to be left with an x. And on the other side,
4 times negative 18. Let's see, that's 40. Well, let's just write it out. So 18 times 4. If we were to multiply 18 times
4, 4 times 8 is 32. 4 times 1 is 4, plus 1 is 72. But this is negative 18 times
4, so it's negative 72. So x is equal to negative 72. And if we want to check it, we
can just substitute it back into that original equation. So let's do that. Let's substitute this into
the original equation. So the original equation was
negative 16 is equal to-- instead of writing x, I'm going
to write negative 72-- is equal to negative
72 over 4 plus 2. Let's see if this is
actually true. So this right-hand side
simplifies to negative 72 divided by 4. We already know that that
is negative 18. So this is equal to negative
18 plus 2. This is what the equation
becomes. And then the right-hand side,
negative 18 plus 2, that's negative 16. So it all comes out true. This right-hand side, when x is
equal to negative 72, does indeed equal negative 16.