You could solve this by guessing and checking, but such a strategy might be difficult for numbers larger or smaller than #-33#. As such, we will use an algebraic approach to solve this.
We are told that the sum of three consecutive integers is #-33#. Let's call the lowest of these three integers #x#. Since the numbers are consecutive, it must be the case that the next smallest integer is #x+1# and the greatest integer is #x+2#.
So we can rewrite the problem as the algebraic statement #x + (x+1) + (x+2) = -33#. The rest is algebra.
#x + (x+1) + (x+2) = -33#
#x + x + 1 + x + 2 = -33#
#3x + 3 = -33#
#3x = -36#
#x = -12#
Our lowest integers is #-12#. It follows that our next two integers are #-11# and #-10#. We confirm that #-12 - 11 - 10 = -23 - 10 = -33#.
