First off, consecutive integer and can be written as n, n+1 and n+2
(try putting a number in for n if it does not make sense yet)
The sum of the first and twice the second would be n+2(n+1)
So, our equation becomes
n+2(n+1)=110-3(n+2)
n+2n+2=110-3n-6
3n+2=104
6n=102
n=17
so, our three term are 17,18 and 19