Your inequality is equivalent to this one

     > 0.


The fraction is positive if and only if the denominator is positive

    2x - 1 > 0.


Add 1 to both sides.  You will get an equivalent inequality

    2x > 1.


Divide both sides by 2.   You will get an equivalent inequality

    x > 1/2.


It is your ANSWER.  In the interval form  (1/2,oo).


In the graph form


    ----------|-----------o=============|========================|====>
              0          1/2            1                        2