Question

1. \\(\frac{p - 5}{p + 1} = \frac{2}{3}\\)

Explanation:

Step1: Cross - multiply the equation

To solve the equation \(\frac{p - 5}{p + 1}=\frac{2}{3}\), 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 \(3(p - 5)=2(p + 1)\).

Step2: Expand both sides

Expand the left - hand side: \(3\times p-3\times5 = 3p-15\). Expand the right - hand side: \(2\times p+2\times1=2p + 2\). Now our equation becomes \(3p-15 = 2p+2\).

Step3: Isolate the variable \(p\)

Subtract \(2p\) from both sides of the equation: \(3p-2p-15=2p - 2p+2\), which simplifies to \(p-15 = 2\). Then add 15 to both sides: \(p-15 + 15=2 + 15\).

Answer:

\(p = 17\)