Solve the inequality $\frac{6x}{4x-1}<\frac{1}{2}$

The correct option is C $x\in (-\frac{1}{8},\frac{1}{4})$
We have,
$\frac{6x}{4x-1}<\frac{1}{2}$

Now,
$\Rightarrow \frac{6x}{4x-1}-\frac{1}{2}<0$
$\Rightarrow \frac{12x-4x+1}{2(4x-1)}<0$
$\Rightarrow \frac{8x+1}{2(4x-1)}\Rightarrow \frac{8x+1}{(4x-1)}<0$
Above inequality is true iff numerator and denominator have different signs.

Case 1 : $8x+1>0$ and $4x-1<0$
$\Rightarrow x>\frac{-1}{8}$ and $x<\frac{1}{4}$
i.e, $x\in (-\frac{1}{8},\frac{1}{4})$

Case 2 : $8x+1<0$ and $4x-1>0$
$\Rightarrow x<\frac{-1}{8}$ and $x>\frac{1}{4}$

No common region,
Hence, there is no solution for case 2.

So, final result will be, $x\in (-\frac{1}{8},\frac{1}{4})$

Hence the correct answer is option (c).