$0,5\times x - \frac{2}{3}\times x = \frac{5}{12}$

$\Leftrightarrow  \frac{1}{2}\times x - \frac{2}{3}\times x = \frac{5}{12}$

$\Leftrightarrow  \frac{3}{6}\times x - \frac{4}{6}\times x = \frac{5}{12}$

$\Leftrightarrow   -\frac{1}{6}\times x = \frac{5}{12}$

$\Leftrightarrow  x = \frac{5}{12} : \frac{-1}{6}$

$\Leftrightarrow  x = \frac{5}{12} \times (-6)$

$\Leftrightarrow  x = \frac{-5}{2}$