To make the fractions \( \frac{7}{14} \) and \( \frac{1}{x} \) equal, we can simplify \( \frac{7}{14} \).
Simplifying \( \frac{7}{14} \) gives us:
\[ \frac{7 \div 7}{14 \div 7} = \frac{1}{2} \]
Now we set this equal to \( \frac{1}{x} \):
\[ \frac{1}{2} = \frac{1}{x} \]
From this, it is clear that \( x = 2 \).
Thus, the missing number is 2.