\[2\frac{2}{3}x - 1\frac{5^{\backslash 3}}{7} = 3\frac{1}{21}\]
\[\frac{8}{3}x = 3\frac{1}{21} + 1\frac{15}{21}\]
\[\frac{8}{3}x = 4\frac{16}{21}\]
\[x = \frac{100 \cdot 3}{21 \cdot 8} = \frac{24}{14}\]
\[x = 1\frac{11}{14}.\]