\(2x-\left|x+1\right|=-\frac{1}{2}\)
=> \(\left|x+1\right|=2x-\left(-\frac{1}{2}\right)\)
=> \(\left|x+1\right|=2x+\frac{1}{2}\)
=> \(\left[{}\begin{matrix}x+1=2x+\frac{1}{2}\\x+1=-\left(2x+\frac{1}{2}\right)\end{matrix}\right.\) => \(\left[{}\begin{matrix}x-2x=\frac{1}{2}-1\\x+1=-2x-\frac{1}{2}\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}-1x=-\frac{1}{2}\\x+2x=\left(-\frac{1}{2}\right)-1\end{matrix}\right.\) => \(\left[{}\begin{matrix}x=\left(-\frac{1}{2}\right):\left(-1\right)\\3x=-\frac{3}{2}\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=\frac{1}{2}\\x=\left(-\frac{3}{2}\right):3\end{matrix}\right.\) => \(\left[{}\begin{matrix}x=\frac{1}{2}\\x=-\frac{1}{2}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{1}{2};-\frac{1}{2}\right\}.\)
Chúc bạn học tốt!
\(2x-\left|x+1\right|=-\frac{1}{2}\)
\(\Leftrightarrow\left|x+1\right|=2x+\frac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=2x+\frac{1}{2}\\x+1=-\left(2x+\frac{1}{2}\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x+1=-2x-\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\3x=-\frac{3}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x=-\frac{1}{2}\end{matrix}\right.\)
Vậy : \(x\in\left\{\frac{1}{2},-\frac{1}{2}\right\}\)