Question

the equation $p = 2l + 2w$ is used to find $p$, the perimeter of a rectangle, using the length ($l$) and the width ($w$) of the rectangle. what is an equivalent equation solved for $w$?
$\bigcirc$ $w = 2(p - 2l)$
$\bigcirc$ $w = \frac{p}{2} - 2l$
$\bigcirc$ $w = \frac{p - 2l}{2}$
$\bigcirc$ $w = p - 2l$

Explanation:

Step1: Isolate the term with $w$

Subtract $2l$ from both sides.
$P - 2l = 2w$

Step2: Solve for $w$

Divide both sides by 2.
$w = \frac{P - 2l}{2}$

Step3: Simplify the expression

Rewrite as separate fractions.
$w = \frac{P}{2} - \frac{2l}{2} = \frac{P}{2} - l$

Answer:

$\boldsymbol{w = \frac{P}{2} - 2l}$ (matches the second option)