1. The problem is to find the value of $x$ in the proportion $\frac{118}{18} = \frac{83}{x}$. 2. The formula for solving proportions is to cross multiply: $a/b = c/d \implies a \times d = b \times c$. 3. Applying cross multiplication here: $118 \times x = 18 \times 83$. 4. Calculate the right side: $18 \times 83 = 1494$. 5. So, $118x = 1494$. To find $x$, divide both sides by 118: $$x = \frac{1494}{118}$$ 6. Simplify the fraction: $1494 \div 118 = 12.66$ (rounded to two decimal places). 7. Therefore, the value of $x$ is approximately $12.66$.