\(2\left|\dfrac{1}{7}-x\right|=\dfrac{4}{3}\Leftrightarrow\left|\dfrac{1}{7}-x\right|=\dfrac{2}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{7}-x=\dfrac{2}{3}\\\dfrac{1}{7}-x=\dfrac{-2}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-11}{21}\\x=\dfrac{17}{21}\end{matrix}\right.\)
\(\Leftrightarrow x_1=\dfrac{-11}{21};x_2=\dfrac{17}{21}\)