<s>[INST] Simple inequality $\frac{4x+1}{2x-3}>2$ 
$$\frac{4x+1}{2x-3}>2$$

I have started with looking at positive/negative situations and there are 2 or that both expressions are positive or both are negative.
If both a positive we can solve for  $$\frac{4x+1}{2x-3}>2$$
 $${4x+1}>2(2x-3)$$
$${4x+1}>4x-6$$
$${0x}>-7$$
Or both are negative and then  $${4x+1}<2(2x-3)$$
And again $$0x<-7$$
So there is not answer?
 [/INST] For $x > \frac{3}{2}$, we rearrange to $$4x+1 > 4x -6 \iff 1 > -6$$ and so it holds for all $x > \frac{3}{2}$.
If $x < \frac{3}{2}$, we rearrange to  $$4x+1 < 4x-6 \iff 1 < -6$$ and hence it does not hold for $x < \frac{3}{2}$.
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