Question

31 solve for x: \\(\frac{12}{x} = \frac{14}{x + 1}\\) (make sure to start your answer with \x = \)

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{12}{x}=\frac{14}{x + 1}\), 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 \(12\times(x + 1)=14\times x\).

Step2: Expand the left - hand side

Expanding \(12\times(x + 1)\) using the distributive property \(a(b + c)=ab+ac\) (here \(a = 12\), \(b=x\), \(c = 1\)), we get \(12x+12 = 14x\).

Step3: Subtract \(12x\) from both sides

Subtract \(12x\) from both sides of the equation \(12x+12 = 14x\) to isolate the variable terms. So, \(12x+12-12x=14x - 12x\), which simplifies to \(12 = 2x\).

Step4: Solve for \(x\)

Divide both sides of the equation \(12 = 2x\) by 2. \(\frac{12}{2}=\frac{2x}{2}\), which gives \(x = 6\).

Answer:

\(x = 6\)