\(A=\left|3-x\right|+\left|x+7\right|+\left|x+1\right|\)
\(A\ge\left|3-x+x+7\right|+\left|x+1\right|=10+\left|x+1\right|\ge10\)
\(A_{min}=10\) khi \(\left\{{}\begin{matrix}\left(3-x\right)\left(x+7\right)\ge0\\\left|x+1\right|=0\end{matrix}\right.\) \(\Rightarrow x=-1\)