\(A=\left|x-1\right|+\left|x-2\right|+\left|x+3\right|\)
\(A=\left|x-1\right|+\left|2-x\right|+\left|x+3\right|\)
\(A\ge\left|x-1\right|+\left|2-x+x+3\right|\)
\(A\ge\left|x-1\right|+5\ge5\)
Dấu "=" xảy ra khi: \(\left\{{}\begin{matrix}-3\le x\le2\\x=1\end{matrix}\right.\)
Vậy \(x=1\) thì \(min_A=5\)