Question

solve for x. \\(\frac{14}{x - 2} = \frac{16}{x - 8}\\) \\(\bigcirc\\) x = 72 \\(\bigcirc\\) x = -72 \\(\bigcirc\\) x = 40 \\(\bigcirc\\) x = -40

Explanation:

Step1: Cross - multiply the equation

To solve the equation \(\frac{14}{x - 2}=\frac{16}{x - 8}\), we cross - multiply. Cross - multiplying gives us \(14(x - 8)=16(x - 2)\).

Step2: Expand both sides

Expand the left - hand side: \(14x-112\), and the right - hand side: \(16x - 32\). So the equation becomes \(14x-112 = 16x-32\).

Step3: Move the x terms to one side

Subtract \(14x\) from both sides: \(-112=16x - 14x-32\), which simplifies to \(-112 = 2x-32\).

Step4: Solve for x

Add 32 to both sides: \(-112 + 32=2x\), so \(-80 = 2x\). Then divide both sides by 2: \(x=\frac{-80}{2}=-40\).

Answer:

D. \(x = - 40\)