Easy as 1, 2, 3?

Algebra Level 4

x+2×x+3×{x}=6\Large { \left \lceil x \right \rceil } + 2 \times {\left \lfloor x \right \rfloor } + 3 \times {\left \{ x \right \} } = 6

How many different values of xx satisfy the equation above?


Notations:

  • x\left \lceil x \right \rceil is the ceiling of x.x.
  • x\left \lfloor x \right \rfloor is the floor of x.x.
  • {x}\left \{ x \right \} is the fractional part of x.x.
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