1. **State the problem:** Solve the equation $$3x + 15 = 3(x + 6) - 3$$. 2. **Apply the distributive property:** Expand the right side: $$3x + 15 = 3 \times x + 3 \times 6 - 3 = 3x + 18 - 3$$ 3. **Simplify the right side:** $$3x + 15 = 3x + 15$$ 4. **Subtract $3x$ from both sides:** $$\cancel{3x} + 15 = \cancel{3x} + 15$$ $$15 = 15$$ 5. **Interpret the result:** Since the variables cancel out and the remaining statement $15 = 15$ is true, the equation holds for all real values of $x$. **Final answer:** Infinitely Many Solutions (All Real Numbers).