Solve for × and give solution in interval notation.

Question

1/|×-4|<1/|×+7|

 

Why is (4,+inf) not in answer and why isn't -(3/2) included

Answer 1

1/|×-4|<1/|×+7| multiply both sides by |×-4|×|×+7| to get

 

|×+7|<|×-4| which says that the points you are looking for are those

whose distance from -7 is less than their distance from 4.

The middle of that interval is the point -3/2.

The points we want are those in -inf<x<-3/2, the half-line closer to -7.