Final answer:
The smallest integer in a set of four consecutive integers that sums to -142 is -37. This was determined by setting the smallest integer as x, writing an equation for the sum of the integers, and solving for x.
Step-by-step explanation:
To find four consecutive integers that sum up to -142, we can let the smallest integer be represented by x. The next three consecutive integers would then be x+1, x+2, and x+3. The sum of these four integers can be written as:
x + (x+1) + (x+2) + (x+3) = -142
We can simplify this equation by combining like terms:
4x + 6 = -142
Subtracting 6 from both sides, we get:
4x = -148
Dividing both sides by 4, we find:
x = -37
Therefore, the smallest consecutive integer is -37.