1. **Problem:** Solve for $n$ in the equation $$3 \left(n + \frac{1}{3}\right) = 7 \left(\frac{n}{2}\right)$$ 2. **Formula and rules:** - Distribute multiplication over addition. - Multiply both sides to clear fractions if needed. - Isolate $n$ to solve. 3. **Step-by-step solution:** 1. Distribute 3 on the left side: $$3n + 3 \times \frac{1}{3} = 7 \times \frac{n}{2}$$ 2. Simplify multiplication: $$3n + 1 = \frac{7n}{2}$$ 3. Multiply both sides by 2 to clear denominator: $$2(3n + 1) = 7n$$ 4. Expand left side: $$6n + 2 = 7n$$ 5. Subtract $6n$ from both sides: $$2 = 7n - 6n$$ 6. Simplify right side: $$2 = n$$ **Final answer:** $$n = 2$$