Comparing asymptotic notations
If P is solvable in $O(n^7)$, that means that P is solvable in $C \cdot n^7$ time, for some constant $C&gt;0$ and large enough $n$. Since $C \cdot n^7 &lt; C \cdot n^9$ for large enough $n$, that implies that P is solvable in $O(n^9)$.

P is bounded by O($n^7$) in the worst case, but it does not imply that in the best case cannot run in constant time, for instance. Thus, P is not greater than $C \cdot n^7$ for large enough $n$, so it is not $\Omega(n^7)$.