Solving for a Letter

Sometimes you want to rearrange a formula so that a different letter is on its own. From $P = 2l+2w$, make a formula for $w$. Treat every other letter as if it were a known number, and undo what is done to $w$. Subtract $2l$ from both sides, then divide both sides by 2:

$$P-2l = 2w$$

$$w = \frac{P-2l}{2}$$

The result is a formula for the width in terms of the perimeter and the length. It is the same equation, solved for $w$ instead of $P$.

Letters such as $P$ and $l$ stand for numbers that have not been given. To get the letter you want on its own, do the same operation to both sides, just as you would with numbers. If you divide both sides by an expression, that expression must not be zero.