1. **State the problem:** Solve the equation $9j + 3 = 3(3j + 1)$. 2. **Write the formula and rules:** Use the distributive property to expand the right side: $a(b + c) = ab + ac$. Then, isolate the variable $j$ by combining like terms and using inverse operations. 3. **Expand the right side:** $9j + 3 = 3 \times 3j + 3 \times 1 = 9j + 3$. 4. **Rewrite the equation:** $9j + 3 = 9j + 3$. 5. **Subtract $9j$ from both sides:** $9j + 3 - 9j = 9j + 3 - 9j$ which simplifies to $3 = 3$. 6. **Interpret the result:** Since $3 = 3$ is always true, the equation holds for all values of $j$. 7. **Final answer:** The solution is all real numbers, or $j \in \mathbb{R}$.