Floor Ceiling Floor Ceiling Floor Ceiling 2

Algebra Level 5

x+12+x+x12x+12+x+x12\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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