1. **State the problem:** We need to find the value of the expression $$\frac{7 - 3x}{2}$$ when $$x = -9$$. 2. **Substitute the value of $$x$$:** Replace $$x$$ with $$-9$$ in the expression: $$\frac{7 - 3(-9)}{2}$$ 3. **Simplify inside the numerator:** Multiply $$-3$$ by $$-9$$: $$\frac{7 + 27}{2}$$ 4. **Add the terms in the numerator:** $$\frac{34}{2}$$ 5. **Divide numerator by denominator:** $$\frac{\cancel{34}}{\cancel{2}} = 17$$ **Final answer:** $$17$$