Đáp án:
\(a,\,\,\,x \ge 5\,\,\,\,hoặc\,\,\,x \le 4\)
\(b,\,\,\,x > 2\,\,\,\,hoặc\,\,\,x < - 3\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\left( {8 - 2x} \right).\left( {3x - 15} \right) \le 0\\
\Leftrightarrow \left[ { - 2.\left( {x - 4} \right)} \right].\left[ {3.\left( {x - 5} \right)} \right] \le 0\\
\Leftrightarrow - 6.\left( {x - 4} \right).\left( {x - 5} \right) \le 0\\
\Leftrightarrow \left( {x - 4} \right).\left( {x - 5} \right) \ge 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 4 \ge 0\\
x - 5 \ge 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 4 \le 0\\
x - 5 \le 0
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \ge 4\\
x \ge 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x \le 4\\
x \le 5
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 5\\
x \le 4
\end{array} \right.\\
Vậy\,\,\,\,x \ge 5\,\,\,\,hoặc\,\,\,x \le 4\\
b,\\
\left( {6 - 3x} \right).\left( {12 + 4x} \right) < 0\\
\Leftrightarrow \left[ { - 3.\left( {x - 2} \right)} \right].\left[ {4.\left( {x + 3} \right)} \right] < 0\\
\Leftrightarrow - 12.\left( {x - 2} \right).\left( {x + 3} \right) < 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {x + 3} \right) > 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 2 > 0\\
x + 3 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 2 < 0\\
x + 3 < 0
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x > 2\\
x > - 3
\end{array} \right.\\
\left\{ \begin{array}{l}
x < 2\\
x < - 3
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x > 2\\
x < - 3
\end{array} \right.\\
Vậy\,\,\,\,x > 2\,\,\,\,hoặc\,\,\,x < - 3
\end{array}\)
