Решите неравенство: 5x/12-(x-2)/4+(x+1)/3<0.

\[\frac{5x}{12} - \frac{x - 2}{4} + \frac{x + 1}{3} < 0\ \ \ \ \ | \cdot 12\]

\[5x - 3 \cdot (x - 2) + 4 \cdot (x + 1) < 0\]

\[5x - 3x + 6 + 4x + 4 < 0\]

\[6x < - 10\]

\[x < - \frac{10}{6}\]

\[x < - 1\frac{2}{3}\]

\[Ответ:x \in \left( - \infty;\ - 1\frac{2}{3} \right).\]