If [x] is the greatest integer less than…
Remember that an integer is a “whole number” (either positive or negative), or 0. Thus, if we want to know the greatest integer less than or equal to, for example, 2.1, the answer would be the integer 2, because the integer 2, in this case, is the largest integer that is less than 2.1. Similarly, the greatest integer less than -2.4 would be -3, because the integer -3 is the largest integer that is less than -2.4. Note that in each case, we have rounded down, because of the “less than” requirement stated in the question stem.
We first need to determine the values for [-1.6], [3.4],and [2.7]. Since the notation [x] means the greatest integer less than or equal to x, we will round down each value in the brackets. Therefore,
[-1.6] = -2
[3.4] = 3
[2.7] = 2
We sum these three integers:
-2 + 3 + 2 = 3