1. We are given the compound inequality $$-14 \leq 7x - 7 \leq 7$$ and need to find the solution set for $x$. 2. The goal is to isolate $x$ in the middle. We start by adding 7 to all parts of the inequality to eliminate the $-7$ term: $$-14 + 7 \leq 7x - 7 + 7 \leq 7 + 7$$ which simplifies to $$-7 \leq 7x \leq 14$$ 3. Next, we divide all parts of the inequality by 7 to solve for $x$. Since 7 is positive, the inequality signs remain the same: $$\frac{-7}{7} \leq \frac{7x}{7} \leq \frac{14}{7}$$ 4. Using the cancellation notation: $$\frac{\cancel{7} \times (-1)}{\cancel{7}} \leq x \leq \frac{\cancel{7} \times 2}{\cancel{7}}$$ which simplifies to $$-1 \leq x \leq 2$$ 5. Therefore, the solution set in interval notation is $$[-1, 2]$$. 6. Since the solution set is not empty, option B ($\emptyset$) is incorrect. Final answer: The solution set is $$[-1, 2]$$.