Question

question 1 1 pt 1 details the length of a rectangle is seven feet less than three times the width. the perimeter is 66 feet. find the width w by solving the equation 2w + 2(3w − 7) = 66. the width is \boxed{} feet.

Explanation:

Step1: Expand the equation

First, we expand the left - hand side of the equation \(2W + 2(3W-7)=66\). Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 2\), \(b=3W\), \(c=- 7\)), we get \(2W+6W - 14=66\).

Step2: Combine like terms

Combine the \(W\) terms: \(2W+6W=8W\), so the equation becomes \(8W-14 = 66\).

Step3: Isolate the variable term

Add 14 to both sides of the equation to isolate the term with \(W\). \(8W-14 + 14=66 + 14\), which simplifies to \(8W=80\).

Step4: Solve for W

Divide both sides of the equation by 8: \(\frac{8W}{8}=\frac{80}{8}\), so \(W = 10\).

Answer:

10