#### Answer

-39, -38, -37

#### Work Step by Step

If we call the first integer x, the next consecutive integer would be x + 1, and the third consecutive integer would be x + 2. If their sum equals -114, the equation is:
x + (x + 1) + (x + 2) = -114
Solve for x:
3x + 3 = -114
3x = -117
x = -39
The first integer is x = -39.
The second integer is x + 1 = -39 + 1 = -38
The third integer is x + 2 = -39 + 2 = -37