Question

1. solve the proportion:

\\(\frac{2}{x + 8} = \frac{4}{x - 1}\\)

Explanation:

Step1: Cross - multiply the proportion

For the proportion $\frac{2}{x + 8}=\frac{4}{x-1}$, cross - multiplying gives us $2(x - 1)=4(x + 8)$.

Step2: Expand both sides

Expand the left - hand side: $2x-2$ and the right - hand side: $4x + 32$. So the equation becomes $2x-2 = 4x+32$.

Step3: Move the x terms to one side

Subtract $2x$ from both sides: $2x-2-2x=4x + 32-2x$, which simplifies to $-2 = 2x+32$.

Step4: Solve for x

Subtract 32 from both sides: $-2-32=2x+32 - 32$, so $-34 = 2x$. Then divide both sides by 2: $x=\frac{-34}{2}=-17$.

Answer:

$x = - 17$