\(\left|\dfrac{x}{2}-\dfrac{2}{3}\right|-\dfrac{1}{2}=\dfrac{5}{6}\)
\(\Rightarrow\left|\dfrac{x}{2}-\dfrac{2}{3}\right|=\dfrac{5}{6}+\dfrac{1}{2}=\dfrac{4}{3}\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{x}{2}-\dfrac{2}{3}=\dfrac{4}{3}\\\dfrac{x}{2}-\dfrac{2}{3}=-\dfrac{4}{3}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\left(\dfrac{4}{3}+\dfrac{2}{3}\right).2=4\\x=\left(-\dfrac{4}{3}+\dfrac{2}{3}\right).2=-\dfrac{4}{3}\end{matrix}\right.\)