\[\frac{5}{16}x + 2\frac{3^{\backslash 2}}{4} = 6\frac{1}{8}\]
\[\frac{5}{16}x = 5\frac{9}{8} - 2\frac{6}{8}\]
\[\frac{5}{16}x = 3\frac{3}{8}\]
\[x = \frac{27 \cdot 16}{5 \cdot 8} = \frac{54}{5}\]
\[x = 10\frac{4}{5}.\]