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Algebra Difficulty 4.5 AIME Find the answer

8. The solution set of the inequality x222x+1\left|x^{2}-2\right| \leqslant 2 x+1 is

A number or a short expression. Spacing and $ signs are ignored.

Solution

8. {x21x3}\{x \mid \sqrt{2}-1 \leqslant x \leqslant 3\}

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8. {x21x3}\{x \mid \sqrt{2}-1 \leqslant x \leqslant 3\}

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.