Answer:
2, 4, 6
Explanation:
You want three consecutive even integers such that the sum of twice the first and three times the second is 4 more than twice the third.
Setup
Let x represent the middle integer. Then the first is (x-2) and the third is (x+2). The given relation is ...
2(x -2) + 3x = 2(x +2) +4
Solution
Simplifying the equation gives ...
2x -4 +3x = 2x +4 +4
5x -4 = 2x +8 . . . . . . . collect terms
3x = 12 . . . . . . . . . . . add 4-2x
x = 4 . . . . . . the middle integer
The integers are 2, 4, 6.
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Additional comment
It often simplifies the equation if the variable is used to represent the middle of the consecutive integers in problems like this. In this particular problem, there is not a great advantage.
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