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⌊x+12⌋+⌈x⌉+⌊x−12⌋≥⌈x+12⌉+⌊x⌋+⌈x−12⌉\left\lfloor x+\dfrac{1}{2}\right\rfloor +\lceil x \rceil+\left\lfloor x-\dfrac{1}{2}\right\rfloor\ge \left\lceil x+\dfrac{1}{2}\right\rceil+\lfloor x \rfloor+\left\lceil x-\dfrac{1}{2}\right\rceil⌊x+21⌋+⌈x⌉+⌊x−21⌋≥⌈x+21⌉+⌊x⌋+⌈x−21⌉ Given that 1≤x≤10001\le x\le 10001≤x≤1000 is a real number, find the number of different xxx's that satisfy the above inequality.
If you believe there are an infinite number of xxx's that satisfy the inequality, then submit −1-1−1.
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