\(\text{| x - 22 | + | x - 3 | + | x - 2017 | = 2014}\)
\(\Leftrightarrow\text{| x - 22 | + | x - 2017 | + | 3 - x | = 2014 }\)
Ta có : \(\left|3-x\right|+\left|x-2017\right|\ge\left|3-x+x-2017\right|=2014\) \(\forall x\in R\)
\(\left|x-22\right|\ge0\)\(\) \(\forall x\in R\)
Dấu " = " xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}\left(3-x\right)\left(x-2017\right)\ge0\\x-22=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3\le x\le2017\\x=22\end{matrix}\right.\)
Vậy \(x=22\)
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