Find 3 consecutive integers such that five times the third integer is eleven less than three times the sum of the first and the second integers

Question

Find 3 consecutive integers such that five times the third integer is eleven less than three times the sum of the first and the second integers

Answer 1

1st is X , 2nd is X+1, 3rd is X+2

5 times the second is equal to 11 less than 3 times the sum of the 1st and 2nd

5(x+2) = 3(x+x+1)-11

5(x+2) = 3 (2x+1) - 11

5x+10 = 6x + 3 - 11

5x+10 = 6x - 8

10 = x-8

x=18

18, 19, and 20

5*20=100

3(18+19)-11 = 3(37)-11 = 111-11 = 100

yes it checks

18, 19, and 20