SOLUTION: Find three consecutive integers such that twice the greatest integer is 2 less than 3 times the least integer. Please help me solve this

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Question 673332: Find three consecutive integers such that twice the greatest integer is 2 less than 3 times the least integer. Please help me solve this
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let the three consecutive integers be n, n%2B1, and n%2B2.
The greatest integer is n%2B2.
Twice the greatest integer is 2%28n%2B2%29.
The least integer is n.
Three times the least integer is 3n.
Then, 2 less than 3 times the least integer is 3n-2
Twice the greatest integer is 2 less than 3 times the least integer
translates as 2%28n%2B2%29=3n-2
2%28n%2B2%29=3n-2 --> 2n%2B4=3n-2 --> 2n%2B4-2n=3n-2-2n --> 4=n-2 --> 4%2B2=n-2%2B2 --> 6=n or highlight%28n=6%29
So the three consecutive integers are highlight%286%29, highlight%287%29, and highlight%288%29.