1. **State the problem:** Solve for $n$ in the equation $$2 - \frac{1}{2}n = 3n + 16$$. 2. **Write down the equation:** $$2 - \frac{1}{2}n = 3n + 16$$. 3. **Goal:** Isolate $n$ on one side. 4. **Move all terms involving $n$ to one side and constants to the other:** $$2 - \frac{1}{2}n - 3n = 16$$ 5. **Combine like terms for $n$:** $$2 - \left(\frac{1}{2}n + 3n\right) = 16$$ $$2 - \frac{7}{2}n = 16$$ 6. **Subtract 2 from both sides:** $$2 - \cancel{2} - \frac{7}{2}n = 16 - 2$$ $$- \frac{7}{2}n = 14$$ 7. **Divide both sides by $-\frac{7}{2}$ to solve for $n$:** $$n = \frac{14}{-\frac{7}{2}}$$ 8. **Simplify the division by multiplying by the reciprocal:** $$n = 14 \times -\frac{2}{7}$$ 9. **Calculate:** $$n = -4$$ **Final answer:** $$n = -4$$