1. **State the problem:** Solve the equation $2-\frac{1}{2}n=3n+16$ for $n$. 2. **Write down the equation:** $$2-\frac{1}{2}n=3n+16$$ 3. **Goal:** Isolate $n$ on one side. 4. **Add $\frac{1}{2}n$ to both sides to move all $n$ terms to the right:** $$2=3n+16+\frac{1}{2}n$$ 5. **Combine like terms on the right:** $$3n+\frac{1}{2}n=\frac{6}{2}n+\frac{1}{2}n=\frac{7}{2}n$$ So, $$2=16+\frac{7}{2}n$$ 6. **Subtract 16 from both sides:** $$2-16=\frac{7}{2}n$$ $$-14=\frac{7}{2}n$$ 7. **Multiply both sides by the reciprocal of $\frac{7}{2}$, which is $\frac{2}{7}$, to solve for $n$:** $$n=-14 \times \frac{2}{7}$$ 8. **Simplify:** $$n=-14 \times \frac{2}{7} = -14 \times \frac{2}{7} = -2 \times 2 = -4$$ **Final answer:** $$n=-4$$