\(\left|2x-1\right|=\left|x-3\right|\)
Bình phương 2 vế ta có:
\(\left(\left|2x-1\right|\right)^2=\left(\left|x-3\right|\right)^2\)
\(\Leftrightarrow4x^2-4x+1=x^2-6x+9\)
\(\Leftrightarrow3x^2+2x-8=0\)
\(\Leftrightarrow3x^2-4x+6x-8=0\)
\(\Leftrightarrow x\left(3x-4\right)+2\left(3x-4\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(3x-4\right)=0\)
\(\Leftrightarrow\left[\begin{matrix}x+2=0\\3x-4=0\end{matrix}\right.\)\(\Leftrightarrow\left[\begin{matrix}x=-2\\x=\frac{4}{3}\end{matrix}\right.\)
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