Solving for a variable | Linear equations | Algebra I | Khan Academy

Solving for a Variable

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Solve P equals 2l plus 2w for l.

So this right here,
this is just the formula

for the perimeter
of a rectangle.

Perimeter is equal
to 2 times the length

plus 2 times the width.

But they just want us to solve
this equation right here,

solve for l.

So let's do that.

So we have P is equal to
2 times l plus 2 times w.

So we need to solve for l.

So let's isolate all of
the l terms on one side.

And the best way, we
could just do that

by leaving it here
on the right and then

getting rid of this 2w.

And the best way to
get rid of this 2w

is to subtract it
from the right.

But if you're going to
subtract it from the right,

you also have to
subtract it from the left

if you want this
equality to hold.

So you have to also
subtract it from the left.

And so the left-hand
side becomes P minus 2w.

And the right-hand
side, you get--

this 2w minus 2w cancels out.

You just have a 2l.

And then if you
want to solve for l,

you just have to divide both
sides of this equation by 2.

You just divide both sides
of this equation by 2.

And we have isolated our l.

We get l is equal to
P minus 2w over 2.

Or if we wanted to
write it the other way,

you could write l is equal
to P minus 2w over 2.

And we are done.