Question

1. \\(\frac{x}{2x + 1} = \frac{16}{40}\\)

Explanation:

Step1: Cross - multiply the proportion

We have the equation \(\frac{x}{2x + 1}=\frac{16}{40}\). By the property of proportions (if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)), we get \(40x=16\times(2x + 1)\).

Step2: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), where \(a = 16\), \(b = 2x\) and \(c = 1\), we have \(40x=32x+16\).

Step3: Subtract \(32x\) from both sides

Subtract \(32x\) from each side of the equation \(40x=32x + 16\) to get \(40x-32x=32x + 16-32x\), which simplifies to \(8x=16\).

Step4: Solve for \(x\)

Divide both sides of the equation \(8x = 16\) by 8. So, \(\frac{8x}{8}=\frac{16}{8}\), which gives \(x = 2\).

Answer:

\(x = 2\)