\(\left|x-2015\right|+\left|x-2016\right|+\left|x-2017\right|\)
\(=\left|x-2015\right|+\left|2017-x\right|+\left|x-2016\right|\)
\(\ge\left|x-2015+2017-x\right|+\left|x-2016\right|=2+\left|x-2016\right|\ge2\)
\("="\Leftrightarrow\left\{{}\begin{matrix}2015\le x\le2017\\x=2016\end{matrix}\right.\Rightarrow x=2016\)