Question

X>1 x<-1 has no solution why

Answer 1

Because there are no numbers that are greater than 1 but also less than -1.  Numbers that are greater than one (x>1), are 2, 3, 4, 5, etc.  Numbers that are less than negative one (x<-1) are -2, -3, -4, -5, etc.  There is no overlap for these two numbers, therefore there is no solution that works for both of the inequalities.