Question

multiple choice question 2 solve for x. \\(\frac{3}{4} = \frac{x}{x + 1}\\) a \\(x = 3\\) b \\(x = 1\\) c \\(x = -1\\) d \\(x = \frac{3}{4}\\)

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{3}{4}=\frac{x}{x + 1}\), cross - multiplying (which is based on the property that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \(3(x + 1)=4x\).

Step2: Expand the left - hand side

Expanding \(3(x + 1)\) using the distributive property \(a(b + c)=ab+ac\) (here \(a = 3\), \(b=x\), \(c = 1\)), we get \(3x+3 = 4x\).

Step3: Solve for \(x\)

Subtract \(3x\) from both sides of the equation \(3x+3 = 4x\). So, \(3x+3-3x=4x - 3x\), which simplifies to \(3=x\) or \(x = 3\).

Answer:

A. \(x = 3\)