Question

Tìm x chứa giá trị tuyệt đối

|x-2|-2x = -1

Answer 1

\(\left|x-2\right|-2x=-1\)

⇒ \(\left|x-2\right|=-1+2x\)

⇒ \(\left[{}\begin{matrix}x-2=-1+2x\\x-2=1-2x\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x-2x=\left(-1\right)+2\\x+2x=1+2\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}-1x=1\\3x=3\end{matrix}\right.\)

⇒ \(\left[{}\begin{matrix}x=1:\left(-1\right)\\x=3:3\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)

Vậy \(x\in\left\{-1;1\right\}.\)

Chúc bạn học tốt!