Take each case seperately:
(x+1)>0
x>-1

(x-7)>0
x>7

This means that
x>-1 and x>7
which is the same as simply saying
x>7 (::7>-1)

Hope this helps,
Prabhat
Answer by khwang(438)   (Show Source): You can put this solution on YOUR website!
From
(x+1)(x-7)>0
two roots of (x+1)(x-7) =0
are 7 and -1.

Use your eyes,you can directly see the solution set is (7,+oo) U (-oo,-1).
(union of two open intervals)

This kind of simple question is not for me.
Since another answer is incomplete(wrong), I just show you the
right answer.
Kenny