9. $\frac{2x - 7}{x + 1}=\frac{3}{2}$

Explanation:

Step1: Cross - multiply

Multiply both sides by (2(x + 1)) to get (3(2x - 7)=5\times2(x + 1)). [3(2x - 7)=10(x + 1)]

Step2: Expand both sides

Use the distributive property (a(b + c)=ab+ac). [6x-21 = 10x+10]

Step3: Move (x) terms to one side

Subtract (6x) from both sides: (-21=10x - 6x+10), which simplifies to (-21 = 4x+10).

Step4: Move constant terms to one side

Subtract 10 from both sides: (-21 - 10=4x), so (-31 = 4x).

Step5: Solve for (x)

Divide both sides by 4: (x=-\frac{31}{4})

Answer:

(x =-\frac{31}{4})