Easy as 1, 2, 3?

Algebra Level 4

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

How many different values of \(x\) satisfy the equation above?

\(\)
Notations:

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