Question

solve the following proportion for the variable x.
\\(\frac{7}{x - 2} = \frac{14}{x}\\)

x = \\(\square\\) (type an integer or a simplified fraction.)

Explanation:

Step1: Cross - multiply the proportion

To solve the proportion \(\frac{7}{x - 2}=\frac{14}{x}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). So, we have \(7\times x = 14\times(x - 2)\).

Step2: Expand the right - hand side

Expand \(14\times(x - 2)\) using the distributive property \(a(b - c)=ab - ac\). Here, \(a = 14\), \(b=x\) and \(c = 2\), so \(14\times(x - 2)=14x-28\). Our equation becomes \(7x=14x - 28\).

Step3: Move the \(x\) terms to one side

Subtract \(7x\) from both sides of the equation \(7x=14x - 28\) to get \(7x-14x=14x - 28-14x\). Simplifying both sides, we have \(- 7x=-28\).

Step4: Solve for \(x\)

Divide both sides of the equation \(-7x=-28\) by \(-7\). \(\frac{-7x}{-7}=\frac{-28}{-7}\), which gives \(x = 4\).

Answer:

\(x = 4\)