Lời giải:
Ta có: \(|3x-2018|+|x-2017|=|3x-2018|+|2017-x|\)
Áp dụng BĐT dạng: \(|a|+|b|\geq |a+b|\) ta có:
\(|3x-2018|+|2017-x|\geq |3x-2018+2017-x|\)
\(\Leftrightarrow |3x-2018|+|2017-x|\geq |2x-1|\)
Dấu bằng xảy ra khi mà: \((3x-2018)(2017-x)\geq 0\)
\(\Leftrightarrow \left[\begin{matrix} 3x-2018\geq 0; 2017-x\geq 0\\ 3x-2018\leq 0; 2017-x\leq 0\end{matrix}\right.\)
\(\Leftrightarrow \left[\begin{matrix} \frac{2018}{3}\leq x\leq 2017\\ \frac{2018}{3}\geq x\geq 2017(\text{vô lý})\end{matrix}\right.\)
Vậy \(\frac{2018}{3}\leq x\leq 2017\)
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