\[x^{2} - 11x + 24 < 0\]
\[x_{1} + x_{2} = 11;\ \ x_{1} \cdot x_{2} = 24\]
\[x_{1} = 3;\ \ x_{2} = 8;\]
\[(x - 3)(x - 8) < 0\]
\[3 < x < 8.\]
\[Ответ:3 < x < 8.\]