To solve for the denominator \( x \) in the proportion \( \frac{21}{3} = \frac{49}{x} \), we can use cross-multiplication.
Starting from the proportion:
\[ \frac{21}{3} = \frac{49}{x} \]
Cross-multiply:
\[ 21 \cdot x = 49 \cdot 3 \]
Now simplify the right side:
\[ 49 \cdot 3 = 147 \]
So the equation now reads:
\[ 21x = 147 \]
Next, solve for \( x \) by dividing both sides by 21:
\[ x = \frac{147}{21} \]
Now, simplify \( \frac{147}{21} \):
\[ x = 7 \]
Thus, the value of \( x \) that would make the ratios proportional is \( \boxed{7} \).