\(2\left|x-3\right|+\left|5-x\right|+\left|x-4\right|\)
\(=\left|2x-6\right|+\left|5-x\right|+\left|4-x\right|\)
\(\ge\left|2x-6+5-x\right|+\left|4-x\right|\)
\(=\left|x-1\right|+\left|4-x\right|\)
\(\ge\left|x-1+4-x\right|=3\)
Đẳng thức xảy ra khi \(\left\{{}\begin{matrix}\left(2x-6\right)\left(5-x\right)\ge0\\\left(x-1\right)\left(4-x\right)\ge0\end{matrix}\right.\Leftrightarrow3\le x\le4\)