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Let {x} and [x] denote the fractional part and the greatest integer (integral part) of a real number x respectively. Solve the equation 4{x} = x + [x].

1. x = 0 and x = 4/3
2. x = 0 and x = 5/3
3. x = 1/3 and x = 5/3
4. x = 0 and x = 1

Correct answer: x = 0 and x = 5/3

Solution

Using x = n + f gives 4f = (n + f) + n = 2n + f, so 3f = 2n, f = 2n/3. The constraint 0 <= f < 1 forces n = 0 or n = 1, yielding the two solutions.

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