Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

\section*{Problem 1 - 300921}

Determine all real numbers x≠3x \neq 3 for which the following inequality (1) holds!

2x−3+12<5x−3−110 \frac{2}{x-3}+\frac{1}{2}<\frac{5}{x-3}-\frac{1}{10}

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

Solution

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The inequality is equivalent to 35x−3>0\frac{3}{5}x-3>0 or 3<x<83<x<8.

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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.