Thay vào:
\(\left|x-1\right|+1-2\left[\left|x-2\right|+2\right]=-3\)
\(\Leftrightarrow\left|x-1\right|-2\left|x-2\right|=-3-1+4=0\Leftrightarrow\)
\(\left|x-1\right|-2\left|x-2\right|=0\)(1)
Chia khoảng \(\left\{\begin{matrix}x< 1\\\left|x-1\right|=1-x\\\left|x-2\right|=2-x\end{matrix}\right.\)\(\Rightarrow\left(1\right)\Leftrightarrow1-x-4+2x=0\Rightarrow x=3>1\)(LOẠI)
\(\left\{\begin{matrix}1\le x< 2\\\left|x-1\right|=x-1\\\left|x-2\right|=2-x\end{matrix}\right.\)\(\Rightarrow x-1-4+2x=0\Rightarrow x=\dfrac{5}{3}< 2\)(NHẬN)
\(\left\{\begin{matrix}x\ge2\\\left|x-1\right|=x-1\\\left|x-2\right|=x-2\end{matrix}\right.\)\(\Rightarrow x-1+4-2x=0\Rightarrow x=3>2\)(nhận)
Kết luận: \(\left[\begin{matrix}x=\dfrac{5}{3}\\x=3\end{matrix}\right.\)
