To solve the equation \( \frac{x}{5.5} = \frac{6}{11} \), we can start by cross-multiplying:
\[ x \cdot 11 = 6 \cdot 5.5 \]
This simplifies to:
\[ 11x = 33 \]
Now, divide both sides by 11 to isolate \( x \):
\[ x = \frac{33}{11} \]
Calculating the division gives:
\[ x = 3 \]
So the solution is:
\[ \boxed{3} \]