\[\left\{ \begin{matrix}
5x + 12 > 0 \\
3x - 4 < 0\ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix}
5x > - 12 \\
3x < 4\ \ \ \ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix}
x > - 2,4 \\
x < 1\frac{1}{3}\text{\ \ \ } \\
\end{matrix} \right.\ \]

\[Ответ:\left( - 2,4;1\frac{1}{3} \right).\]