1. **State the problem:** Solve the equation $$-\frac{1}{2}x - 3 = 4$$ for $x$. 2. **Add 3 to both sides** to isolate the term with $x$: $$-\frac{1}{2}x - 3 + 3 = 4 + 3$$ $$-\frac{1}{2}x = 7$$ 3. **Divide both sides by $-\frac{1}{2}$** to solve for $x$: $$x = \frac{7}{-\frac{1}{2}}$$ 4. **Simplify the division by a fraction** by multiplying by its reciprocal: $$x = 7 \times \left(-2\right)$$ 5. **Calculate the product:** $$x = -14$$ **Final answer:** $$x = -14$$