This question would have been definitely better as a Quantitative Comparison question where the question taker has to figure out how the value of x could affect the median of the set of numbers.

Since it is numerical entry question then you know there is a definite answer and you shouldn't consider the value of x as relevant.

The logical reasoning for this problem is as follows.

We should divide into some cases after we put numbers in ascending order.
We have numbers $7, 7, 9, 9, 9, 11, 15$ and $x$.

Case 1) $x \le 7$
Then we have $x, 7, 7, 9, 9, 9, 11, 15$ in ascending order and their median is $9$.

Case 2) $7 < x \le 9$
Then we have $7, 7, x, 9, 9, 9, 11, 15$ in ascending order and their median is $9$.

Case 3) $9 < x \le 11$
Then we have $7, 7, 9, 9, 9, x, 11, 15$ in ascending order and their median is $9$.

Case 4) $11 < x \le 15$
Then we have $7, 7, 9, 9, 9, 11, x, 15$ in ascending order and their median is $9$.

Case 5) $15 < x$
Then we have $7, 7, 9, 9, 9, 11, 15, x$ in ascending order and their median is $9$.

All cases tell $9$ is their median, whatever $x$ is.