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Algebra Difficulty 4.9 AIME Find the answer

(3) Given that 3 is a solution to the inequality (xa)(x+2a1)2(x3a)0(x-a)(x+2 a-1)^{2}(x-3 a) \leqslant 0, find the range of real values for aa.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

(3) {1}[1,3]\{-1\} \cup[1,3]

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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.