\(\left|x+\dfrac{1}{7}\right|-\dfrac{2}{3}=0\)
\(\Rightarrow\left|x+\dfrac{1}{7}\right|=0+\dfrac{2}{3}\\ \Rightarrow\left|x+\dfrac{1}{7}\right|=\dfrac{2}{3}\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{7}=\dfrac{2}{3}\\x+\dfrac{1}{7}=-\dfrac{2}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}-\dfrac{1}{7}\\x=-\dfrac{2}{3}-\dfrac{1}{7}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{21}\\x=-\dfrac{17}{21}\end{matrix}\right.\)