1)
$|x+\frac{1}{7}|-\frac{2}{3}=-0$
$|x+\frac{1}{7}| = \frac{2}{3}$
\(\left[ \begin{array}{l}x+\frac{1}{7}=\frac{2}{3}\\x+\frac{1}{7}=-\frac{2}{3}\end{array} \right.\)
\(\left[ \begin{array}{l}x=\frac{11}{21}\\x=-\frac{17}{21}\end{array} \right.\)
2)
$|x+\frac{1}{3}|-4= -1$
$|x+\frac{1}{3}|= 3$
\(\left[ \begin{array}{l}x+\frac{1}{3}=3\\x+\frac{1}{3}=-3\end{array} \right.\)
\(\left[ \begin{array}{l}x=\frac{8}{3}\\x=-\frac{10}{3}\end{array} \right.\)