Question

solve for w.
\\(\frac{4}{w - 2} = \frac{3}{5}\\)
simplify your answer as much as possible.
\\(w = \square\\)

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{4}{w - 2}=\frac{3}{5}\), cross - multiplying (which is based on the property that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \(4\times5 = 3\times(w - 2)\).
So, \(20=3(w - 2)\).

Step2: Distribute the 3

Using the distributive property \(a(b - c)=ab - ac\), we expand \(3(w - 2)\) to get \(3w-6\). So the equation becomes \(20 = 3w-6\).

Step3: Add 6 to both sides

To isolate the term with \(w\), we add 6 to both sides of the equation. \(20 + 6=3w-6 + 6\), which simplifies to \(26 = 3w\).

Step4: Divide both sides by 3

Divide both sides of the equation \(26 = 3w\) by 3. So, \(w=\frac{26}{3}\) (or we can write it as a mixed number \(8\frac{2}{3}\), but the improper fraction is also a simplified form).

Answer:

\(\frac{26}{3}\) (or \(8\frac{2}{3}\))