1. **State the problem:** Find the solution set of the inequality $x - 9 < -15$ where $x$ is an integer. 2. **Write the inequality:** $$x - 9 < -15$$ 3. **Isolate $x$ by adding 9 to both sides:** $$x - 9 + 9 < -15 + 9$$ $$x < -6$$ 4. **Interpret the solution:** The solution set includes all integers less than $-6$. 5. **Express the solution set:** $$\{x \in \mathbb{Z} \mid x < -6\} = \{..., -8, -7\}$$ 6. **Match with given options:** - Option A: $\{-8, -7, -6, ...\}$ includes $-6$ and numbers greater than $-6$, so incorrect. - Option B: $\{-9, -8, -7, ...\}$ includes $-7$ and numbers greater than $-7$, so incorrect. - Option C: $\{..., -8, -7, -6\}$ includes $-6$, so incorrect. - Option D: $\{..., -9, -8, -7\}$ includes all integers less than $-6$, so correct. **Final answer:** Option D