3 consecutive integers are such that three times the smallest is 14 more than the largest. find the integers.
You have three consecutive numbers: $\displaystyle n, (n+1), (n+2)$
3 times the smallest is 14 more than the largest: $\displaystyle 3n=14+(n+2)$
Thus: $\displaystyle 3n=n+16$
Therefore: $\displaystyle 2n=16$
Finally: $\displaystyle n=8$
So the numbers are: 8, 9, and 10.