Question

1. \\(\frac{x - 3}{18} = \frac{12}{9}\\)

Explanation:

Step1: Cross - multiply the fractions

To solve the proportion \(\frac{x - 3}{18}=\frac{12}{9}\), 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 \((x - 3)\times9=18\times12\).

Step2: Simplify both sides

First, calculate the right - hand side: \(18\times12 = 216\). The left - hand side is \(9(x - 3)\). So our equation becomes \(9(x - 3)=216\).

Step3: Divide both sides by 9

Divide both sides of the equation \(9(x - 3)=216\) by 9. \(\frac{9(x - 3)}{9}=\frac{216}{9}\), which simplifies to \(x - 3 = 24\).

Step4: Solve for x

Add 3 to both sides of the equation \(x - 3 = 24\). \(x-3 + 3=24 + 3\), so \(x = 27\).

Answer:

\(x = 27\)