Bài giải:

$\left| 2x-\frac{1}{2} \right|+\frac{3}{7}=5\frac{3}{7}$

$\Rightarrow \left| 2x-\frac{1}{2} \right|+\frac{3}{7}=\frac{38}{7}$

$\Rightarrow \left| 2x-\frac{1}{2} \right|=\frac{38}{7}-\frac{3}{7}$

$\Rightarrow \left| 2x-\frac{1}{2} \right|=5$

$\Rightarrow \left[ \begin{align}& 2x-\frac{1}{2}=5 \\ & 2x-\frac{1}{2}=-5 \\ \end{align} \right.$            

$\Rightarrow \left[ \begin{align}& 2x=5+\frac{1}{2} \\ & 2x=-5+\frac{1}{2} \\\end{align} \right.$               

$\Rightarrow \left[ \begin{align}& 2x=\frac{11}{2} \\ & 2x=\frac{-9}{2} \\\end{align} \right.$             

$\Rightarrow \left[ \begin{align}& x=\frac{11}{4} \\ & x=\frac{-9}{4} \\\end{align} \right.$

Mà: x < 0

Vậy: $x=\frac{-9}{4}$