So let's call the smallest of the three integers a.
Therefore,
(a) + (a+1) + (a+2) = -114.
Combining the like terms, we get:
3a + 3 = -114
Subtracting 3 on both sides to leave the variables on one side, we get:
3a = -117
Finally, dividing both sides by 3 to isolate the variable, we have:
a = -13.
Therefore, the smallest of the integers is -13.
Since our original equation was:
(a) + (a+1) + (a+2) = -114,
we plug -13 for each time we see a.
Therefore, the three integers are:
-13, -12, and -11.
