9514 1404 393
Answer:
- (x -3) +(x -1) +(x +1) +(x +3) = -72
- -21, -19, -17, -15
Explanation:
Let x represent the even integer between the middle two odd integers. Then the sum of the four odd integers is ...
(x -3) +(x -1) +(x +1) +(x +3) = -72
4x = -72
x = -18
The four integers are -21, -19, -17, -15.
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Additional comment
You could let x represent one of the integers. Often, people choose to let it represent the least of them. Then the equation becomes x +(x+2) +(x+4) +(x+6) = -72, so 4x = -84 and x = -21. This introduces a "subtract 12" step in the solution process that is unnecessary if x is chosen to be the average of the integers.
As the average, x is the sum divided by the number of them, so you know x=-72/4 = -18 immediately. Then you just have to find the nearest two odd integers below and above -18. You can do the whole problem mentally.