You have the following opeartion between sets:
(x + 2 < 5) U (x - 7 > 6)
In order to find the solution to the previoues expression, you first find the solutionof each inequality, just as follow:
x + 2 < 5 subtract 2 both sides
x < 5 - 2
x < 3
The solution interval is (-∞,3)
x - 7 > - 6 add 7 both sides
x > - 6 + 7
x > 1
The solution interval is (1, ∞)
Then, you have:
(-∞,3) U (1,∞)
which is the same that:
{x| x<3 or x>1}
