1. **State the problem:** Simplify the expression $2(x+3) + 1$. 2. **Use the distributive property:** Multiply $2$ by each term inside the parentheses. $$2(x+3) = 2 \times x + 2 \times 3 = 2x + 6$$ 3. **Add the remaining term:** Now add $1$ to the result. $$2x + 6 + 1$$ 4. **Combine like terms:** $6 + 1 = 7$, so the expression simplifies to $$2x + 7$$ 5. **Final answer:** The simplified form of $2(x+3) + 1$ is $$2x + 7$$