Question

question
solve for x and simplify the answer fully.
\\(\frac{x + 3}{x - 1} = \frac{5}{9}\\)

Explanation:

Step1: Cross - multiply the fractions

To solve the equation \(\frac{x + 3}{x - 1}=\frac{5}{9}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\).
Applying this to our equation, we get \(9(x + 3)=5(x - 1)\).

Step2: Expand both sides

Expand the left - hand side: \(9x+27\), and the right - hand side: \(5x - 5\). So the equation becomes \(9x + 27=5x-5\).

Step3: Subtract \(5x\) from both sides

Subtracting \(5x\) from both sides gives \(9x-5x + 27=5x-5x-5\), which simplifies to \(4x+27=-5\).

Step4: Subtract 27 from both sides

Subtract 27 from both sides: \(4x+27 - 27=-5 - 27\), so \(4x=-32\).

Step5: Divide both sides by 4

Divide both sides of the equation \(4x=-32\) by 4: \(\frac{4x}{4}=\frac{-32}{4}\), which gives \(x = - 8\).

Answer:

\(x=-8\)