Which set of numbers best describes the possible values of x in the equation? lceil x minus 1 rceil is equal to lfloor x rfloor

Write x as an integer n plus a fractional part r, where 0 ≤ r < 1. If x is not an integer, then 0 < r < 1, so x − 1 lies between n − 1 and n; its ceiling is n, which also equals the floor of x. If x is an integer, the ceiling of x − 1 is x − 1, not x, so the equation does not hold. Thus the possible values are only noninteger values of x.

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