Question

solve the proportion.
\\(\frac{2}{3} = \frac{10}{x + 5}\\)
\\(x = \square\\) (type an integer or a simplified fraction.)

Explanation:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{2}{3}=\frac{10}{x + 5}\), by the cross - multiplication property of proportions (if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)), we have \(2\times(x + 5)=3\times10\).

Step2: Simplify both sides

First, simplify the left - hand side: \(2(x + 5)=2x+10\), and the right - hand side is \(3\times10 = 30\). So the equation becomes \(2x+10 = 30\).

Step3: Solve for x

Subtract 10 from both sides of the equation: \(2x+10-10=30 - 10\), which simplifies to \(2x=20\). Then divide both sides by 2: \(\frac{2x}{2}=\frac{20}{2}\), so \(x = 10\).

Answer:

\(10\)