Solve (x + 1 < 4) ∩ (x - 8 > -7). {x | 1 < x < 3} {x | x < 3 or x > 1} {all real numbers}

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}