Find three consecutive odd integers such that the sum of the smaller two is three times the largest increased by seven

Let the three odd integers be x - 2, x and x + 2

x - 2 + x = 3 (x + 2) + 7

2x - 2 = 3x + 6 + 7

2x - 2 = 3x + 13

3x - 2x = - 2 - 13

x = - 15

The three consecutive odd integers are - 17, - 15 and - 13.