The sum of three consecutive integers is -165, what is the closest to zero?

Let us assume the smallest of the three consecutive integers = x
Then
The middle integer among the three consecutive integers will be = x + 1
The biggest integer among the three consecutive integers will be = x + 2
The sum of the three consecutive integers is already given in the question and it is -165.
Then
x + x + 1 + x + 2 = - 165
3x + 3 = - 165
3x = - 165 - 3
3x = - 168
x = - (168/3)
   = - 56
So the integer that is closest to zero is - 56. This is the answer you were looking for hopefully. The other integers will obviously be at a greater distance from zero.

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The solution to the system of equations (-2,2)