\(\left|\left|x+1\right|+3\left|-2\right|x-2\right|=3\)(1) \(\left|-2\right|=2\)
\(\left(1\right)\Leftrightarrow A=\left|\left|x+1\right|+6x-2\right|=3\)(2)
xét khoảng: \(x< -1\Rightarrow\left|x+1\right|=-x-1\) \(A=\left|-x-1+6x-2\right|=\left|5x-3\right|\)
\(\left(2\right)\Leftrightarrow\left|5x-3\right|=3\)\(\Rightarrow\left[\begin{matrix}5x-3=3\\5x-3=-3\end{matrix}\right.\)\(\Rightarrow\left[\begin{matrix}x=-\dfrac{6}{5}>-1\\x=0>-1\end{matrix}\right.\) Loại
xét khoảng: \(-1\le x\Rightarrow\left|x+1\right|=x+1\)
\(A=\left|x+1+6x-2\right|=\left|7x-1\right|\)
(2) \(\Leftrightarrow\left[\begin{matrix}7x-1=3\\7x-1=-3\end{matrix}\right.\)\(\Rightarrow\left[\begin{matrix}x=\dfrac{4}{7}\\x=-\dfrac{2}{7}\end{matrix}\right.\) Nhận hết
Kết luận nghiệm là: \(\left[\begin{matrix}x=\dfrac{4}{7}\\x=-\dfrac{2}{7}\end{matrix}\right.\)
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