\(\left|9-7x\right|=5x-3\)
th1 : \(9-7x\ge0\Leftrightarrow7x\le9\Leftrightarrow x\le\dfrac{9}{7}\)
thì \(\left|9-7x\right|=5x-3\Leftrightarrow9-7x=5x-3\)
\(\Leftrightarrow5x-3-9+7x=0\Leftrightarrow12x-12=0\)
\(\Leftrightarrow12x=12\Leftrightarrow x=1\) (tmđk)
th2 : \(9-7x< 0\Leftrightarrow7x>9\Leftrightarrow x>\dfrac{9}{7}\)
thì \(\left|9-7x\right|=5x-3\Leftrightarrow7x-9=5x-3\)
\(\Leftrightarrow7x-9-5x+3=0\Leftrightarrow2x-6=0\)
\(\Leftrightarrow2x=6\Leftrightarrow x=3\) (tmđk)
vậy \(x=1;x=3\)
\(\left|9-7x\right|=5x-3\)
+) TH1: \(9-7x\ge0\Rightarrow x\le\dfrac{9}{7}\)
Khi đó: \(9-7x=5x-3\)
\(\Rightarrow-7x-5x=-9-3\)
\(\Rightarrow-12x=-12\)
\(\Rightarrow x=1\) (thỏa mãn)
+) TH2: \(9-7x< 0\Rightarrow x>\dfrac{9}{7}\)
Khi đó: \(-9+7x=5x-3\)
\(\Rightarrow7x-5x=9-3\)
\(\Rightarrow2x=7\)
\(\Rightarrow x=\dfrac{7}{2}\) (TM)
Vậy \(x\in\left\{1;\dfrac{7}{2}\right\}.\)
\(|9-7x|=5x-3\left(x\ge\dfrac{3}{5}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}9-7x=5x-3\\9-7x=-5x+3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-7x-5x=-3-9\\-7x+5x=3-9\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-12x=-12\\-2x=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
Vậy x=1;x=3
