The sum of three consecutive integers is negative 114 find the integers

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.