9.1. Find the smallest integer $x$ that satisfies the inequality $\frac{100}{|x|}>x^{2}+1$.
Answer: -4.

If $|x| \geq 5$, then $\frac{100}{|x|} \leq \frac{100}{5}=20 \leq 17 = (-4)^{2} + 1$ we verify the correctness of the answer.

Comment. The correct answer without a rigorous justification up to 2 points. The inequality is solved, but the wrong answer is chosen 2 points.