Đáp án:
\(x \in \left\{ { - 2016;\,\,674} \right\}\)
Giải thích các bước giải:
\(\begin{array}{l}
\left| {x - 1} \right| + \left| {x - 2} \right| + x = 2019\,\,\,\,\left( * \right)\\
TH1:\,\,\,x < 1\\
\Rightarrow \left\{ \begin{array}{l}
\left| {x - 1} \right| = - x + 1\\
\left| {x - 2} \right| = - x + 2
\end{array} \right.\\
\Rightarrow \left( * \right) \Leftrightarrow - x + 1 - x + 2 + x = 2019\\
\Leftrightarrow - x = 2016\,\,\,\\
\Leftrightarrow x = - 2016\,\,\,\,\,\left( {tm} \right)\\
TH2:\,\,1 \le x < 2\\
\Rightarrow \left\{ \begin{array}{l}
\left| {x - 1} \right| = x - 1\\
\left| {x - 2} \right| = - x + 2
\end{array} \right.\\
\Rightarrow \left( * \right) \Leftrightarrow x - 1 - x + 2 + x = 2019\\
\Leftrightarrow x = 2018\,\,\,\left( {ktm} \right)\\
TH3:\,\,x \ge 2\\
\Rightarrow \left\{ \begin{array}{l}
\left| {x - 1} \right| = x - 1\\
\left| {x - 2} \right| = x - 2
\end{array} \right.\\
\Rightarrow \left( * \right) \Leftrightarrow x - 1 + x - 2 + x = 2019\\
\Leftrightarrow 3x = 2022\\
\Leftrightarrow x = 674.\\
Vay\,\,\,x \in \left\{ { - 2016;\,\,674} \right\}.
\end{array}\)
