1. **State the problem:** Prove that for any non-negative integer $n$, the expression $32n + 7$ is divisible by 8. 2. **Recall divisibility rules and formulas:** A number $a$ is divisible by $b$ if $a = b \times k$ for some integer $k$. 3. **Analyze the expression:** Consider $32n + 7$. 4. **Check divisibility of each term by 8:** - $32n$ is divisible by 8 because $32 = 8 \times 4$, so $32n = 8 \times 4n$. - $7$ is not divisible by 8. 5. **Combine terms:** Since $32n$ is divisible by 8 but $7$ is not, their sum $32n + 7$ is not divisible by 8. 6. **Conclusion:** The statement that $32n + 7$ is divisible by 8 is false for all $n$. **Final answer:** $32n + 7$ is **not** divisible by 8 for any non-negative integer $n$.