In order to solve this problem, we can refer to the properties of triangles. Recall that the third side of a triangle must be less than the sum of the two known sides, and greater than the difference.
We know that the smallest $y$ can be is $2 x$.

If we set $y=2 x$, and we know that the third side must be greater than the difference between the two known sides, then we know that the third side must be greater than $y-x$; through substitution, this becomes:

third side $\(>2 x-x\)$

third side $\(>x\)$

So we know that the third side must be greater than $x$. However, because we know that $\(y \geq 2 \mathrm{x}\)$, the sum of the two sides can be anything greater than $\(3 x\)$, and so there is no upper limit: $y$ could equal $5 x$, or $200 x$, or $\(1,000 x\)$, etc.

For example, if we set $y=1,000 x$, then the third side would have to be less than the sum of the other two sides:
third side $\(<1,000 x+x\)$

third side \(< 1,001x\)


We see that the upper limit can always get higher, but the third side can never be less than $x$.
So (B), (C), and (D) are the correct answers.