1. **State the problem:** Solve the inequality $x^2 \le 100$. 2. **Recall the rule:** For any real number $x$, $x^2 \le a^2$ implies $-a \le x \le a$ when $a \ge 0$. 3. **Apply the rule:** Here, $a = 10$ because $100 = 10^2$. 4. **Write the solution:** $$-10 \le x \le 10$$ 5. **Explain:** This means $x$ can be any number between $-10$ and $10$, inclusive, because squaring any number in this range will give a value less than or equal to $100$. **Final answer:** $$\boxed{-10 \le x \le 10}$$