Question

1. \\(\frac{9}{10} = \frac{x}{52}\\)\
2. \\(\frac{x - 3}{18} = \frac{12}{9}\\)\
3. \\(\frac{7}{11} = \frac{18}{x + 1}\\)\
4. \\(\frac{3x - 4}{14} = \frac{9}{10}\\)\
5. \\(\frac{17}{35} = \frac{36}{3x - 2}\\)\
6. \\(\frac{x - 16}{x + 6} = \frac{3}{5}\\)\
7. \\(\frac{6}{9} = \frac{x + 12}{2x - 2}\\)\
8. \\(\frac{x - 9}{15} = \frac{2x + 9}{10}\\)

Explanation:

Let's solve problem 14: $\boldsymbol{\frac{x - 3}{18}=\frac{12}{9}}$

Step 1: Cross - multiply

Cross - multiplying the proportion $\frac{a}{b}=\frac{c}{d}$ gives $a\times d = b\times c$. So for $\frac{x - 3}{18}=\frac{12}{9}$, we have $(x - 3)\times9=18\times12$.

Step 2: Simplify both sides

First, calculate the right - hand side: $18\times12 = 216$. The left - hand side is $9(x - 3)=9x-27$. So the equation becomes $9x - 27 = 216$.

Step 3: Solve for x

Add 27 to both sides of the equation: $9x-27 + 27=216 + 27$. This simplifies to $9x=243$. Then divide both sides by 9: $x=\frac{243}{9}=27$.

Answer:

$x = 27$