1. **State the problem:** Solve the inequality $x - 8 > 1$ for $x$. 2. **Recall the rule:** To solve inequalities, you can add or subtract the same number on both sides without changing the inequality direction. 3. **Add 8 to both sides:** $$x - 8 + 8 > 1 + 8$$ which simplifies to $$x > 9$$ 4. **Interpretation:** The solution is all values of $x$ greater than 9. 5. **Final answer:** $$x > 9$$