Note we can get two inequalities out of this:

  AND 

So we write:

 AND 

Add -3x to both sides of the first inequality.
Multiply the second inequality through by 2 to
clear of fractions:

 AND 

Divide the first inequality through by 
which reverses the sign of inequality:
Add  to both sides of the second

 AND 

Simplify the first and divide the second through
by 6 (which BTW does not reverse the sign of
inequality):

 AND 

It's easier to see if we change the
improper fractions to mixed fractions

 AND 

As you can see this is a contradiction because
the same value of x cannot be to the right of
  AND also to the left of .

Thus the solution set is the empty, or null, set, Ø

Edwin