Question

solve for x and simplify the answer fully.
\\(\frac{9}{x - 1} = \frac{5}{2x - 5}\\)
answer attempt 1 out of 1
x =

Explanation:

Step1: Cross - multiply the fractions

To solve the equation \(\frac{9}{x - 1}=\frac{5}{2x - 5}\), 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 \(9\times(2x - 5)=5\times(x - 1)\).

Step2: Expand both sides

Expand the left - hand side: \(9\times(2x-5)=9\times2x-9\times5 = 18x-45\).
Expand the right - hand side: \(5\times(x - 1)=5x-5\).
Now our equation becomes \(18x-45 = 5x-5\).

Step3: Isolate the variable terms

Subtract \(5x\) from both sides of the equation: \(18x-5x-45=5x - 5x-5\), which simplifies to \(13x-45=-5\).
Then add 45 to both sides of the equation: \(13x-45 + 45=-5 + 45\), which gives \(13x=40\).

Step4: Solve for x

Divide both sides of the equation by 13: \(x=\frac{40}{13}\).

Answer:

\(x = \frac{40}{13}\)