1. **State the problem:** Solve the compound inequality $x - 6 < -9$ and $-1 + x \geq -7$. 2. **Solve each inequality separately:** - For $x - 6 < -9$: $$x - 6 < -9$$ Add 6 to both sides: $$x - \cancel{6} + \cancel{6} < -9 + 6$$ $$x < -3$$ - For $-1 + x \geq -7$: $$-1 + x \geq -7$$ Add 1 to both sides: $$-1 + \cancel{x} + 1 \geq -7 + 1$$ $$x \geq -6$$ 3. **Combine the inequalities:** Since the compound inequality uses "and", the solution is the intersection of $x < -3$ and $x \geq -6$. 4. **Write the solution set:** $$-6 \leq x < -3$$ 5. **Explain the graph:** - Closed circle at $-6$ because $x$ can be equal to $-6$. - Open circle at $-3$ because $x$ must be less than $-3$, not equal. - Shade the region between $-6$ and $-3$. **Final answer:** $$\boxed{-6 \leq x < -3}$$