1. **State the problem:** Solve the inequality $$\frac{1}{3}n - 10 > 22$$. 2. **Formula and rules:** To solve inequalities, we perform operations to isolate the variable on one side. When multiplying or dividing by a positive number, the inequality direction stays the same. 3. **Add 10 to both sides:** $$\frac{1}{3}n - 10 + 10 > 22 + 10$$ $$\frac{1}{3}n > 32$$ 4. **Multiply both sides by 3 to clear the fraction:** $$3 \times \frac{1}{3}n > 3 \times 32$$ $$\cancel{3} \times \frac{1}{\cancel{3}} n > 96$$ $$n > 96$$ 5. **Final answer:** $$n > 96$$ This means the variable $n$ must be greater than 96 to satisfy the inequality.