Recall that you can take any integer x, and turn it into an even integer by multiplying it by 2. Thus, you can always make it odd, by multiplying it by 2, and then adding 1. Thus, 2x + 1 is always odd.
So, if you want three consecutive odd integers, you can select:
(1) 2x + 1
(2) 2x + 1 + 2 = 2x + 3
(3) 2x + 1 + 2 + 2 = 2x + 5
Now just add them together and set them equal to -45:
(2x + 1) + (2x + 3) + (2x + 5) = 6x + 9,
so 6x + 9 = -45. Now solve, to find that x = -9.
Now remember that x = -9 is not our answer, we have to use x to find the first consecutive odd: 2*-9 + 1 = -17. Our next two consecutive odds are then -15, and -13.
Check to see if these sum to -45? -17 + -15 + -13 = -45, check!
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