Question

the length of a rectangle is seven feet less than eight times the width. the perimeter is 112 feet. find the width w by solving the equation 2w + 2(8w - 7) = 112. the width is feet.

Explanation:

Step1: Expand the equation

First, we expand the term \(2(8W - 7)\) using the distributive property \(a(b - c)=ab - ac\). So we have:
\(2W+2\times8W-2\times7 = 112\)
\(2W + 16W-14=112\)

Step2: Combine like terms

Next, we combine the \(W\) terms. \(2W+16W = 18W\), so the equation becomes:
\(18W-14 = 112\)

Step3: Isolate the variable term

We add 14 to both sides of the equation to isolate the term with \(W\):
\(18W-14 + 14=112 + 14\)
\(18W=126\)

Step4: Solve for \(W\)

Finally, we divide both sides by 18 to solve for \(W\):
\(W=\frac{126}{18}\)
\(W = 7\)

Answer:

7