Question 126673
If the first odd integer is x, the second one would be x + 2, and the third one would be x + 4.


The sum of the three is {{{x + (x + 2) + (x + 4)}}} but this is equal to 3 times the third odd integer {{{3(x+4)}}}


{{{x + (x + 2) + (x + 4)=3(x+4)}}} 


{{{3x+6=3x+12}}}


Adding -3x to both sides of the equation leads to the absurdity that {{{6=12}}}.  Therefore, there is no solution to the problem as stated.


Had the problem said 3 times the SECOND integer we would have achieved the result that {{{6=6}}} -- true no matter what x is.  Meaning that any three consecutive odd integers would exhibit the property that their sum is equal to 3 times the second integer.  In fact, any three consecutive EVEN integers, or just any three consecutive integers also exhibit the same property.