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Algebra Level 5

x+12xx12x+12xx12\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 Given that 1x10001\le x\le 1000 is a real number, find the number of different xx's that satisfy the above inequality.

If you believe there are an infinite number of xx's that satisfy the inequality, then submit 1-1.

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