let 'x', 'y' and 'z' be the numbers, and we can assume x<=y<=z

the sum of three numbers is 11

x + y + z = 11

the largest number is fourteen more than three times the smallest number

z = 14 + 3x

the middle number is nine more than twice the smallest number

y = 9 + 2x

by solving the system of equations

x + y + z = 11

z = 14 + 3x

y = 9 + 2x

we get

x = -2

y = 5

z = 8

the numbers are -2, 5 and 8.