Question

The formula for the perimeter of a rectangle is$P=2w+2l$, where w represents the width and $l$represents the length. Solve for $w$.

Short answer

The equation for $w$is $\mathit{w}\mathbf{=}\frac{\mathbf{P}\mathbf{-}\mathbf{2}\mathbf{l}}{\mathbf{2}}$.

Step-by-step solution

Step 1. State the concept used.

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similarsign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Step 2. Rewrite the equation to solve for w. 

In order to solve the given equation$P=2w+2l$for the variable, isolate the variable term $w$on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate$w$on both sides, first subtract both sides by $2l$.

$$\begin{gathered} P-2l=2w+2l-2l \\ P-2l=2w \end{gathered}$$

Step 3. Simplify further for w.

Now to further simplifydivide both sides by 2.

$$\begin{gathered} P-2l=2w \\ \frac{P-2l}{2}=\frac{2w}{2} \\ w=\frac{P-2l}{2} \end{gathered}$$