Question

solve for w.
\\(\frac{4}{3} = \frac{8}{w - 2}\\)
simplify your answer as much as possible.
\\(w = \square\\)

Explanation:

Step1: Cross - multiply the equation

To solve the equation \(\frac{4}{3}=\frac{8}{w - 2}\), we can use cross - multiplication. Cross - multiplication states that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\).
Applying this to our equation, we get \(4\times(w - 2)=3\times8\).

Step2: Simplify both sides of the equation

First, simplify the left - hand side: \(4\times(w - 2)=4w-8\).
Simplify the right - hand side: \(3\times8 = 24\). So our equation becomes \(4w-8 = 24\).

Step3: Solve for w

Add 8 to both sides of the equation: \(4w-8 + 8=24 + 8\).
This simplifies to \(4w=32\).
Then divide both sides by 4: \(\frac{4w}{4}=\frac{32}{4}\).
We get \(w = 8\).

Answer:

\(w = 8\)