Solve P = 2(l + w) for l

Step by step

The question

Question: solve for l in P = 2(l + w).

We treat the other letters like numbers.

1 l on the left

l is on the right.

We swap the two sides, so l is on the left.

They are still equal.

2 Remove the 2

2(l + w) means 2 times the bracket.

We want what is in the bracket.

To remove times 2, we divide by 2.

We do it on both sides.

2 divided by 2 is 1.

The bracket is left.

Now we have l + w = P over 2.

3 Remove the + w

We want l by itself.

The w is in the way.

To remove w, we take away w.

We do it on both sides.

They make zero.

Cross them out.

So l = P over 2 − w.

4 Check

Let's check with numbers.

We pick P = 6, w = 2.

Our answer gives l = 1.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are 6.

So our answer is right!

Let's look back.

First: l on the left.

Then: remove the 2.

Then: remove the + w.

Last: check.