Final answer:
By setting up an equation with the smallest integer as n, the four consecutive integers with a sum of -126 are found to be -33, -32, -31, and -30.
Step-by-step explanation:
To find 4 consecutive integers that have a sum of -126, let's denote the smallest integer as n. The next three integers would then be n+1, n+2, and n+3, since they are consecutive.
The sum of these four integers can be represented by the following equation:
n + (n + 1) + (n + 2) + (n + 3) = -126
Combine like terms to simplify:
4n + 6 = -126
Subtract 6 from both sides:
4n = -132
Divide both sides by 4 to find the value of n:
n = -33
Now we have the smallest integer. The other three consecutive integers are:
n+1 = -33 + 1 = -32
n+2 = -33 + 2 = -31
n+3 = -33 + 3 = -30
So, the 4 consecutive integers are -33, -32, -31, and -30.