Yes, you have correctly found the intersection of the two solutions. In interval notation:
Find the set of values of x for which
both 3(2x+1)>5-2x AND 2x^2-7x+3>0
So the answer to the first one is x>1/4, answer to the second is x<1/2 and x>3
But since these conflict, how would I write it?
I think I need to do 1/4<x<1/2 AND x>3
Is this right? Thanks for your help