Giải thích các bước giải:
\(\begin{array}{l}
a,\\
\left\{ \begin{array}{l}
{x^2} + 6x + 5 > 0\\
{x^2} + x - 6 < 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left( {x + 1} \right)\left( {x + 5} \right) > 0\\
\left( {x + 3} \right)\left( {x - 2} \right) < 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x > - 1\\
x < - 5
\end{array} \right.\\
- 3 < x < 2
\end{array} \right. \Leftrightarrow - 3 < x < - 1\\
b,\\
\left\{ \begin{array}{l}
2{x^2} + x - 6 > 0\\
3{x^2} + 3 \ge 10x
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left( {2x - 3} \right)\left( {x + 2} \right) > 0\\
\left( {x - 3} \right)\left( {3x - 1} \right) \ge 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x > \frac{3}{2}\\
x < - 2
\end{array} \right.\\
\left[ \begin{array}{l}
x > 3\\
x < \frac{1}{3}
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x > 3\\
x < - 2
\end{array} \right.\\
c,\\
\left\{ \begin{array}{l}
2{x^2} + 5x > 4\\
{x^2} + 3x < 10
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x > \frac{{ - 5 + \sqrt {57} }}{4}\\
x < \frac{{ - 5 - \sqrt {57} }}{4}
\end{array} \right.\\
- 5 < x < 2
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\frac{{ - 5 + \sqrt {57} }}{4} < x < 2\\
- 5 < x < \frac{{ - 5 - \sqrt {57} }}{4}
\end{array} \right.\\
d,\\
\left\{ \begin{array}{l}
4x - 7 < {x^2}\\
{x^2} - 2x - 1 \ge 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{x^2} - 4x + 7 > 0\\
\left[ \begin{array}{l}
x \ge 1 + \sqrt 2 \\
x \le 1 - \sqrt 2
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x \ge 1 + \sqrt 2 \\
x \le 1 - \sqrt 2
\end{array} \right.
\end{array}\)
