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x that satisfy floor inequality

Source: S&M 2002 1st Grade P1

May 14, 2021
algebrafloor functioninequalities

Problem Statement

Determine all real numbers xx such that 2002⌊x⌋⌊−x⌋+x>⌊2x⌋x−⌊1+x⌋.\frac{2002\lfloor x\rfloor}{\lfloor-x\rfloor+x}>\frac{\lfloor2x\rfloor}{x-\lfloor1+x\rfloor}.
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