\(\Leftrightarrow\left|\dfrac{1}{2}-x\right|=\dfrac{16}{3}\\ \Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}-x=\dfrac{16}{3}\\\dfrac{1}{2}-x=-\dfrac{16}{3}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{29}{6}\\x=\dfrac{35}{6}\end{matrix}\right.\)
\(\Leftrightarrow\left|x-\dfrac{1}{2}\right|=6-\dfrac{2}{3}=\dfrac{16}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{16}{3}\\x-\dfrac{1}{2}=-\dfrac{16}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{35}{6}\\x=-\dfrac{29}{6}\end{matrix}\right.\)
\(\dfrac{2}{3}+\left|\dfrac{1}{2}-x\right|=6\)
\(\Rightarrow\left|\dfrac{1}{2}-x\right|=6-\dfrac{2}{3}=\dfrac{18}{3}-\dfrac{2}{3}=\dfrac{16}{3}\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{1}{2}-x=\dfrac{16}{3}\\\dfrac{1}{2}-x=-\dfrac{16}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{29}{6}\\x=\dfrac{35}{6}\end{matrix}\right.\)
