1. **State the problem:** Solve the equation $3(14n+3) - 2(21n + 4) = 1$ for $n$. 2. **Apply the distributive property:** Multiply inside the parentheses: $$3 \times 14n + 3 \times 3 - 2 \times 21n - 2 \times 4 = 1$$ which simplifies to $$42n + 9 - 42n - 8 = 1$$ 3. **Combine like terms:** Notice $42n - 42n = 0$, so the equation reduces to $$9 - 8 = 1$$ which simplifies to $$1 = 1$$ 4. **Interpret the result:** Since the equation simplifies to a true statement independent of $n$, this means the original equation is true for all values of $n$. **Final answer:** The equation holds for all real numbers $n$; that is, the solution is all real $n$.