Question

solve for x.
\\(\frac{5}{x - 5} = \frac{10}{x - 6}\\)
\\(x = \square\\)

Explanation:

Step1: Cross - multiply the fractions

To solve the equation \(\frac{5}{x - 5}=\frac{10}{x - 6}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). So, we have \(5\times(x - 6)=10\times(x - 5)\).

Step2: Expand both sides

Expand the left - hand side: \(5(x - 6)=5x-30\).
Expand the right - hand side: \(10(x - 5)=10x - 50\).
Now our equation becomes \(5x-30 = 10x-50\).

Step3: Move the variable terms to one side

Subtract \(5x\) from both sides of the equation: \(5x-30-5x=10x - 50-5x\).
This simplifies to \(-30 = 5x-50\).

Step4: Solve for x

Add 50 to both sides of the equation: \(-30 + 50=5x-50 + 50\).
We get \(20 = 5x\).
Then divide both sides by 5: \(\frac{20}{5}=\frac{5x}{5}\), which gives \(x = 4\).

Answer:

\(x = 4\)