Evaluate Using the Given Value Solve P=2l+2w for l

Solve $P = 2 l + 2 w$ for $l$

Step 1

Rewrite the equation as $2 l + 2 w = P$ .

$2 l + 2 w = P$

Step 2

Subtract $2 w$ from both sides of the equation.

$2 l = P - 2 w$

Step 3

Divide each term in $2 l = P - 2 w$ by $2$ and simplify.

Divide each term in $2 l = P - 2 w$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $l$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 w$ .

$l = \frac{P}{2} + \frac{2 (- w)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$l = \frac{P}{2} + \frac{2 (- w)}{2 (1)}$

Cancel the common factor.

$l = \frac{P}{2} + \frac{2 (- w)}{2 \cdot 1}$

Rewrite the expression.

$l = \frac{P}{2} + \frac{- w}{1}$

Divide $- w$ by $1$ .

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