Nhờ anh chị giải giùm bài dưới đây, xin cám ơn nhiều: Tìm x sao cho (1 - |x| ) ( x + 1) > 0

Đáp án:

\(x \in \left( { - \infty ;\,\,1} \right)\backslash \left\{ { - 1} \right\}\)

Giải thích các bước giải: \(\begin{array}{l} \left( {1 - \left| x \right|} \right)\left( {x + 1} \right) > 0\\ \Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} 1 - \left| x \right| > 0\\ x + 1 > 0 \end{array} \right.\\ \left\{ \begin{array}{l} 1 - \left| x \right| < 0\\ x + 1 < 0 \end{array} \right. \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} \left| x \right| < 1\\ x > - 1 \end{array} \right.\\ \left\{ \begin{array}{l} \left| x \right| > 1\\ x < - 1 \end{array} \right. \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} - 1 < x < 1\\ x > - 1 \end{array} \right.\\ \left\{ \begin{array}{l} \left[ \begin{array}{l} x > 1\\ x < - 1 \end{array} \right.\\ x < - 1 \end{array} \right. \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} - 1 < x < 1\\ x < - 1 \end{array} \right..\\ \Rightarrow x \in \left( { - \infty ;\,\,1} \right)\backslash \left\{ { - 1} \right\}. \end{array}\)