The condition of the problem is AMBIGOUS. It can be read, translated and interpreted in two different ways. One way is 3(x+2) - 4 = 2(x+2) + 15. The other way is 3(x+2) - 4 = 2*((x+2) + 15). Different equations/translations/interpretations produce different answers.
Your 3 integers are CORRECT!
You need to check the book again, to make sure you're looking at the answers for this particular problem!