1. **State the problem:** We need to find the left-hand limit of the piecewise function $$f(x)$$ as $$x$$ approaches 3 from the left, i.e., $$\lim_{x \to 3^-} f(x)$$. 2. **Identify the relevant piece:** Since we are approaching 3 from the left ($$x < 3$$), we use the piece $$f(x) = 3x - 7$$. 3. **Apply the limit:** Substitute $$x = 3$$ into $$3x - 7$$ to find the limit. $$\lim_{x \to 3^-} f(x) = 3(3) - 7 = 9 - 7 = 2$$ 4. **Conclusion:** The left-hand limit of $$f(x)$$ as $$x$$ approaches 3 is $$2$$. Therefore, the answer is **2**.