Ta có :
\(\left|x-1\right|=\left|1-x\right|\)
\(\Leftrightarrow\left|x-1\right|+\left|x+3\right|=\left|1-x\right|+\left|x+3\right|\ge\left|1-x+x+3\right|\)
\(\Leftrightarrow\left|x-1\right|+\left|x+3\right|\ge\left|4\right|\)
\(\Leftrightarrow\left|x-1\right|+\left|x+3\right|\ge4\)
Dấu "=" xảy ra \(\Leftrightarrow\left(1-x\right)\left(x+3\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}1-x\ge0\\x+3\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}1-x\le0\\x+3\le0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}1\ge x\\x\ge-3\end{matrix}\right.\\\left\{{}\begin{matrix}1\le x\\x\le-3\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}1\ge x\ge-3\\x\in\varnothing\end{matrix}\right.\)
Vậy..
