Question 352194
By multiplying the denominator, you lose the information contained within it. 
Numbers are OK since you know the value, but variable expressions are unknown (could be positive, could be negative).
Go this way instead.
{{{(4x)/(2x+3)>2}}}
{{{(4x)/(2x+3)-2>0}}}
{{{(4x)/(2x+3)-((2(2x+3))/(2x+3))>0}}}
{{{(4x)/(2x+3)-((4x+6)/(2x+3))>0}}}
{{{(4x-(4x+6))/(2x+3))>0}}}
{{{(4x-4x-6)/(2x+3))>0}}}
{{{(-6)/(2x+3))>0}}}
which holds when 
{{{2x+3<0}}}
{{{2x<-3}}}
{{{highlight(x<-3/2)}}}
.
.
.
{{{drawing(300,300,-10,10,-10,10,blue(line(-3/2,10,-3/2,-10)),graph(300,300,-10,10,-10,10,(4x)/(2x+3),2))}}}