Question

the length of a rectangle is two feet less than three times the width. the perimeter is 44 feet. find the width ( w ) by solving the equation ( 2w + 2(3w - 2) = 44 ). the width is (\boxed{quad}) feet.

Explanation:

Step1: Expand the equation

First, we expand \(2(3W - 2)\) using the distributive property \(a(b - c)=ab - ac\). So, \(2(3W - 2)=2\times3W-2\times2 = 6W - 4\). The original equation \(2W + 2(3W - 2)=44\) becomes \(2W+6W - 4 = 44\).

Step2: Combine like terms

Combine the \(W\) terms: \(2W+6W = 8W\). So the equation is now \(8W - 4 = 44\).

Step3: Isolate the variable term

Add 4 to both sides of the equation to isolate the term with \(W\). \(8W-4 + 4=44 + 4\), which simplifies to \(8W=48\).

Step4: Solve for \(W\)

Divide both sides by 8: \(\frac{8W}{8}=\frac{48}{8}\), so \(W = 6\).

Answer:

6