The Correct Answer and Explanation is:
The correct answer is -38.
To solve this problem, we need to identify a set of four even integers that are consecutive and sum up to -164. Consecutive even integers are even numbers that follow each other in order, with each number being two greater than the previous one, for example, 2, 4, 6, and 8.
We can represent these unknown integers using algebra. Let’s define the smallest of the four integers as ‘x’. Because they are consecutive even integers, the next three numbers in the set will be x + 2, x + 4, and x + 6. The question asks for the greatest integer, which in this representation would be x + 6.
The problem states that the sum of these four numbers is -164. We can set up an equation to reflect this:
x + (x + 2) + (x + 4) + (x + 6) = -164
Next, we solve this equation for x. First, we combine all the ‘x’ terms and all the constant numbers on the left side of the equation:
4x + 12 = -164
To isolate the ‘4x’ term, we subtract 12 from both sides of the equation:
4x = -164 – 12
4x = -176
Now, we can find the value of x by dividing both sides by 4:
x = -176 / 4
x = -44
This means the smallest integer in the set is -44. We can now find all four integers:
- First integer: x = -44
- Second integer: x + 2 = -42
- Third integer: x + 4 = -40
- Fourth (greatest) integer: x + 6 = -38
The set of integers is -44, -42, -40, and -38. As a final check, their sum is -44 + (-42) + (-40) + (-38) = -164. The calculation is correct. The greatest integer in this set is -38.
