Solve P = 2l + 2w for w

Step by step

The question

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

We treat the other letters like numbers.

1 w on the left

w is on the right.

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

They are still equal.

2 Remove the 2l

We want w by itself.

The 2l is in the way.

To remove 2l, we take away 2l.

We do it on both sides.

They make zero.

Cross them out.

Now we have 2w = P − 2l.

3 Remove the 2

2w means 2 times w.

We want just w.

To remove times 2, we divide by 2.

We do it on both sides.

2 divided by 2 is 1.

So just w is left.

So w = (P − 2l)/2.

4 Check

Let's check with numbers.

We pick P = 6, l = 2.

Our answer gives w = 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: w on the left.

Then: remove the 2l.

Then: remove the 2.

Last: check.