Đáp án:
c. \(\left\{ \begin{array}{l}
x < \dfrac{{20}}{7}\\
x > 2
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne 2\\
A = \dfrac{{ - x + 3}}{{x - 2}}\\
A \ge 1\\
\to \dfrac{{ - x + 3}}{{x - 2}} \ge 1\\
\to \dfrac{{ - x + 3 - x + 2}}{{x - 2}} \ge 0\\
\to \dfrac{{ - 2x + 5}}{{x - 2}} \ge 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
- 2x + 5 \ge 0\\
x - 2 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
- 2x + 5 \le 0\\
x - 4 < 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \le - \dfrac{5}{2}\\
x > 2
\end{array} \right.\left( l \right)\\
\left\{ \begin{array}{l}
x \ge - \dfrac{5}{2}\\
x < 4
\end{array} \right.
\end{array} \right.\\
\to - \dfrac{5}{2} \le x < 4\\
A < \dfrac{1}{5}\\
\to \dfrac{{ - x + 3}}{{x - 2}} < \dfrac{1}{5}\\
\to \dfrac{{ - 5x + 15 - x + 2}}{{5\left( {x - 2} \right)}} < 0\\
\to \dfrac{{ - 6x + 17}}{{5\left( {x - 2} \right)}} < 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
- 6x + 17 > 0\\
x - 2 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
- 6x + 17 < 0\\
x - 2 > 0
\end{array} \right.
\end{array} \right.\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x < \dfrac{{17}}{6}\\
x < 2
\end{array} \right.\\
\left\{ \begin{array}{l}
x > \dfrac{{17}}{6}\\
x > 2
\end{array} \right.
\end{array} \right.\\
\to \left[ \begin{array}{l}
x > \dfrac{{17}}{6}\\
x < 2
\end{array} \right.\\
A > \dfrac{1}{6}\\
\to \dfrac{{ - x + 3}}{{x - 2}} > \dfrac{1}{6}\\
\to \dfrac{{ - 6x + 18 - x + 2}}{{6\left( {x - 2} \right)}} > 0\\
\to \dfrac{{ - 7x + 20}}{{6\left( {x - 2} \right)}} > 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
- 7x + 20 > 0\\
x - 2 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
- 7x + 20 < 0\\
x - 2 < 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x < \dfrac{{20}}{7}\\
x > 2
\end{array} \right.\\
\left\{ \begin{array}{l}
x > \dfrac{{20}}{7}\\
x < 2
\end{array} \right.\left( l \right)
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x < \dfrac{{20}}{7}\\
x > 2
\end{array} \right.
\end{array}\)
