Question

solve for x and simplify the answer fully.
\\(\frac{5}{x - 8} = \frac{8}{x - 2}\\)
answer attempt 1 out of 3
x =

Explanation:

Step1: Cross - multiply the fractions

To solve the equation \(\frac{5}{x - 8}=\frac{8}{x - 2}\), we use the cross - multiplication property of fractions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). So, we have \(5(x - 2)=8(x - 8)\).

Step2: Expand both sides

Expand the left - hand side: \(5(x - 2)=5x-10\).
Expand the right - hand side: \(8(x - 8)=8x - 64\).
So the equation becomes \(5x-10 = 8x-64\).

Step3: Move the x - terms to one side and constants to the other

Subtract \(5x\) from both sides: \(5x-10-5x=8x - 64-5x\), which simplifies to \(- 10 = 3x-64\).
Then add 64 to both sides: \(-10 + 64=3x-64 + 64\), so \(54 = 3x\).

Step4: Solve for x

Divide both sides by 3: \(\frac{54}{3}=\frac{3x}{3}\), which gives \(x = 18\).

Answer:

\(x = 18\)