Solve 2[x] = x + {x}, where [.] and {.} denote the greatest integer function and the fractional part function, respectively.
Answer & explanation
Correct answer: option 1
Given $2[x] = x + \{x\}$
or $2[x] = [x] + 2\{x\}$
or $\{x\} = \frac{[x]}{2}$
or $0≤\frac{[x]}{2}<1$
or $0≤[x]<2$
or [x] = 0, 1
For [x] = 0, we get {x} = 0 or x = 0.
For [x] = 1, we get $\{x\} = \frac{1}{2}$ or $x = \frac{3}{2}$