3 < 3x - 3 ≤ 2x + 2
Adding -3 to each side gives
0 < 3x - 6 ≤ 2x - 1
The left inequality says
0 < 3x - 6 ⇒ 3x > 6 ⇒ x > 2
while the right inequality says
3x - 6 ≤ 2x - 1 ⇒ x ≤ 5
Then the solutions belong to the interval 2 < x ≤ 5 and contains only the integers x = 3, x = 4, and x = 5.