\[5\frac{1}{4}x - 2\frac{2^{\backslash 4}}{3} = 1\frac{5}{12}\]
\[\frac{21}{4}x = 1\frac{5}{12} + 2\frac{8}{12}\]
\[\frac{21}{4}x = 3\frac{13}{12}\]
\[x = \frac{49 \cdot 4}{12 \cdot 21}\]
\[x = \frac{7}{9}.\]