\(5-\left|2x-7\right|=3x-4\\ \Leftrightarrow\left|2x-7\right|=9-3x\)
\(TH1:\\ \begin{matrix}2x-7=9-3x\\9-3x\ge0\end{matrix}\Leftrightarrow\begin{matrix}5x=2\\3x\le9\end{matrix}\Leftrightarrow\begin{matrix}x=\dfrac{2}{5}\\x\le3\end{matrix}\Leftrightarrow x=\dfrac{2}{5}\)(2 biếu thức trên - dưới là dấu và)
\(TH2:\Leftrightarrow\left\{{}\begin{matrix}2x-7=3x-9\\9-3x< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\x>3\end{matrix}\right.\Leftrightarrow x\in\varnothing\)
Cách 2:
|2x-7|=9-3x
Vì |2x-7| >=0 => 9-3x >=0 => x<=3
=> 2x-7<= -1 < 0
=> |2x-7|=7-2x
=> 7-2x = 9-3x
=> x=2 (thỏa mãn)
\(5-\left|2x-7\right|=3x-4\)
\(\Leftrightarrow\left|2x-7\right|=5-3x+4=9-3x\)
TH1 : \(2x-7=9-3x\Leftrightarrow5x=16\Leftrightarrow x=\dfrac{16}{5}\)
TH2 : \(2x-7=-9+3x\Leftrightarrow-x=-2\Leftrightarrow x=2\)
