1. **State the problem:** Solve the equation $$\frac{1}{2} q = -24$$ for the variable $q$. 2. **Formula and rules:** To isolate $q$, multiply both sides of the equation by the reciprocal of $\frac{1}{2}$, which is 2. 3. **Intermediate work:** $$\cancel{\frac{1}{2}} q \times 2 = -24 \times 2$$ This simplifies to: $$q = -48$$ 4. **Explanation:** Multiplying both sides by 2 cancels the $\frac{1}{2}$ coefficient on $q$, leaving $q$ alone on the left side. Multiplying $-24$ by 2 gives $-48$. 5. **Final answer:** $$q = -48$$