Evaluate: {\text{begin}array l 4x-x^2 <= 0 } x^2-2x-3 > 0 10+3x-x^2 > 0\text{end}array .

Expression: $\left\{\begin{array} { l } 4x-{x}^{2} \leq 0 \\ {x}^{2}-2x-3 > 0 \\ 10+3x-{x}^{2} > 0\end{array} \right.$

Solve the inequality for $x$

$\left\{\begin{array} { l } x \in \left\langle-\infty, 0\right] \cup \left[ 4, +\infty\right\rangle \\ {x}^{2}-2x-3 > 0 \\ 10+3x-{x}^{2} > 0\end{array} \right.$

Solve the inequality for $x$

$\left\{\begin{array} { l } x \in \left\langle-\infty, 0\right] \cup \left[ 4, +\infty\right\rangle \\ x \in \langle-\infty, -1\rangle \cup \langle3, +\infty\rangle \\ 10+3x-{x}^{2} > 0\end{array} \right.$

Solve the inequality for $x$

$\left\{\begin{array} { l } x \in \left\langle-\infty, 0\right] \cup \left[ 4, +\infty\right\rangle \\ x \in \langle-\infty, -1\rangle \cup \langle3, +\infty\rangle \\ x \in \langle-2, 5\rangle\end{array} \right.$

Find the intersection

$x \in \langle-2, -1\rangle \cup \left[ 4, 5\right\rangle$