|5x−3|=|7x−2|
\(\left[{}\begin{matrix}5x-3=7x-2\\5x-3=2-7x\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}2x=-1\\12x=5\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=\dfrac{5}{12}\end{matrix}\right.\)
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2.|x−1|=|3x+7|
\(\Leftrightarrow\)4(x-1)2=(3x+7)2
\(\Leftrightarrow\)4x2-8x+4=9x2+42x+49
\(\Leftrightarrow\)5x2+50x+45=0
\(\Leftrightarrow\)x2+10x+9=0
\(\Leftrightarrow\)x2+9x+x+9=0
\(\Leftrightarrow\)x(x+9)+(x+9)=0
\(\Leftrightarrow\)(x+1)(x+9)=0
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x+1=0\\x+9=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=-1\\x=-9\end{matrix}\right.\)
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