When solved
(x + 1 < 4) ∩ (x - 8 > -7)
becomes:
(x+1-1 < 4-1) ∩ (x - 8 +8 > -7+8 )
(x < 3) ∩ (x > 1).
and if you change places it will become even more obvious:
( 1<x ) ∩ ( x < 3 )
meaning: x is set of all numbers greater than 1 and less than 3 or otherwise:
{x | 1 < x < 3}
