Giải thích các bước giải: Ta có: $\begin{array}{l}\left( { – 2} \right)\left| {x – 1} \right| – 3\left| {5 – x} \right| < – 22\\ \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}x \ge 5\\ – 2\left( {x – 1} \right) – 3\left( {x – 5} \right) < – 22\end{array} \right.\\\left\{ \begin{array}{l}1 \le x < 5\\ – 2\left( {x – 1} \right) – 3\left( {5 – x} \right) < – 22\end{array} \right.\\\left\{ \begin{array}{l}x < 1\\ – 2\left( {1 – x} \right) – 3\left( {5 – x} \right) < – 22\end{array} \right.\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}x \ge 5\\ – 5x < – 39\end{array} \right.\\\left\{ \begin{array}{l}1 \le x < 5\\x < – 9\end{array} \right.\\\left\{ \begin{array}{l}x < 1\\5x < – 5\end{array} \right.\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}x \ge 5\\x > \dfrac{{39}}{5}\end{array} \right.\\\left\{ \begin{array}{l}1 \le x < 5\\x < – 9\end{array} \right.\left( l \right)\\\left\{ \begin{array}{l}x < 1\\x < – 1\end{array} \right.\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x > \dfrac{{39}}{5}\\x < – 1\end{array} \right.\end{array}$ Vậy $x > \dfrac{{39}}{5}$ hoặc $x < – 1$ thỏa mãn đề Reply
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
\left( { – 2} \right)\left| {x – 1} \right| – 3\left| {5 – x} \right| < – 22\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \ge 5\\
– 2\left( {x – 1} \right) – 3\left( {x – 5} \right) < – 22
\end{array} \right.\\
\left\{ \begin{array}{l}
1 \le x < 5\\
– 2\left( {x – 1} \right) – 3\left( {5 – x} \right) < – 22
\end{array} \right.\\
\left\{ \begin{array}{l}
x < 1\\
– 2\left( {1 – x} \right) – 3\left( {5 – x} \right) < – 22
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \ge 5\\
– 5x < – 39
\end{array} \right.\\
\left\{ \begin{array}{l}
1 \le x < 5\\
x < – 9
\end{array} \right.\\
\left\{ \begin{array}{l}
x < 1\\
5x < – 5
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \ge 5\\
x > \dfrac{{39}}{5}
\end{array} \right.\\
\left\{ \begin{array}{l}
1 \le x < 5\\
x < – 9
\end{array} \right.\left( l \right)\\
\left\{ \begin{array}{l}
x < 1\\
x < – 1
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x > \dfrac{{39}}{5}\\
x < – 1
\end{array} \right.
\end{array}$
Vậy $x > \dfrac{{39}}{5}$ hoặc $x < – 1$ thỏa mãn đề