$\begin{array}{l} \left\{ \begin{array}{l} x - 3 \le 0\\ {x^2} + 2x > 0 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} x \le 3\\ x\left( {x + 2} \right) > 0 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} x \le 3\\ \left[ \begin{array}{l} x > 0\\ x \le - 2 \end{array} \right. \end{array} \right. \Rightarrow \left[ \begin{array}{l} 0 < x \le 3\\ x \le - 2 \end{array} \right.\\ \Rightarrow x \in \left( {0;3} \right] \cup \left( { - \infty ; - 2} \right] \end{array}$
