Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.1 AIME, harder Find the answer

(2) Given the inequality $\frac{a x-1}{x}>2 a$ with the solution set $M$ , and $2 \notin M$ , find the range of real number $a$ .

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.

Your answer

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

Solution

(2) $\left[-\frac{1}{2},+\infty\right)$

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