$\frac{2}{3}-\left| 2x-\frac{3}{4} \right|=\frac{1}{2}$

$\left| 2x-\frac{3}{4} \right|=\frac{2}{3}-\frac{1}{2}$

$\left| 2x-\frac{3}{4} \right|=\frac{1}{6}$

$2x-\frac{3}{4}=\pm \frac{1}{6}$

TH1:

$2x-\frac{3}{4}=\frac{1}{6}$

$2x=\frac{1}{6}+\frac{3}{4}$

$2x=\frac{11}{12}$

$x=\frac{11}{24}$

*TH2:

$2x-\frac{3}{4}=-\frac{1}{6}$

$2x=-\frac{1}{6}+\frac{3}{4}$

$2x=\frac{7}{12}$

$x=\frac{7}{24}$

Vậy đáp án đúng là đáp án A.