1) \(\left|9-7x\right|=5x-3\)
\(\Rightarrow\left|9-7x\right|-5x=-3\)
\(\Leftrightarrow\left[{}\begin{matrix}9-7x-5x=-3\left(đk:9-7x\ge0\right)\\-\left(9-7x\right)-5x=-3\left(đk:9-7x< 0\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(đk:x\le\dfrac{9}{7}\right)\\x=3\left(đk:x>\dfrac{9}{7}\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
Vậy \(x_1=1;x_2=3\)
2) \(8x-\left|4x+1\right|=x+2\)
\(\Rightarrow8x-\left|4x+1\right|-x=2\)
\(\Leftrightarrow7x-\left|4x+1\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}7x-\left(4x+1\right)=2\left(đk:4x+1\ge0\right)\\7x-\left(-\left(4x+1\right)\right)=2\left(đk:4x+1< 0\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(đk:x\ge-\dfrac{1}{4}\right)\\x=\dfrac{1}{11}\left(đk:x< -\dfrac{1}{4}\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x\in\varnothing\end{matrix}\right.\)
Vậy \(x=1\)
3) \(\left|17x-5\right|-\left|17x+5\right|=0\)
\(\Rightarrow\left|17x-5\right|=\left|17x+5\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}17x-5=17x+5\\17x-5=-\left(17x+5\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x\in\varnothing\\x=0\end{matrix}\right.\)
Vậy \(x=0\)
4) \(\left|3x+4\right|=2\left|2x-9\right|\)
\(\Rightarrow\left[{}\begin{matrix}3x+4=2\left(2x-9\right)\\3x+4=-2\left(2x-9\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=22\\x=2\end{matrix}\right.\)
Vậy \(x_1=2;x_2=22\)
