Question

2x-|x-1|=1/2

Answer 1

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Answer 2

\(\Leftrightarrow\left|x-1\right|=2x-\dfrac{1}{2}\\ \Leftrightarrow\left[{}\begin{matrix}x-1=2x-\dfrac{1}{2},\forall x\ge1\\x-1=\dfrac{1}{2}-2x,\forall x< 1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2},\forall x\ge1\left(L\right)\\x=\dfrac{1}{2},\forall x< 1\left(N\right)\end{matrix}\right.\\ \Leftrightarrow x=\dfrac{1}{2}\)