Question

question 1
the length of a rectangle is six feet less than two times the width. the perimeter is 12 feet. find the width w by solving the equation 2w + 2(2w - 6) = 12.
the width is feet.
check answer
question 2
solve.
\\(\frac{2x + 7}{9} = \frac{x}{8}\\)
x =
check answer

Explanation:

Question 1

Step1: Simplify the left side

First, expand \(2(2W - 6)\) to get \(4W - 12\). Then the equation \(2W + 2(2W - 6)=12\) becomes \(2W + 4W - 12 = 12\). Combine like terms: \(6W - 12 = 12\).

Step2: Solve for W

Add 12 to both sides: \(6W - 12 + 12 = 12 + 12\), so \(6W = 24\). Divide both sides by 6: \(W=\frac{24}{6}=4\).

Step1: Cross - multiply

Cross - multiply the equation \(\frac{2x + 7}{9}=\frac{x}{8}\) to get \(8(2x + 7)=9x\).

Step2: Expand and solve

Expand the left side: \(16x+56 = 9x\). Subtract \(16x\) from both sides: \(16x + 56-16x=9x - 16x\), which gives \(56=-7x\). Divide both sides by \(- 7\): \(x=\frac{56}{-7}=-8\).

Answer:

4

Question 2