\(\left|x-5\right|-x=3\)
\(\Rightarrow\left|x-5\right|=3+x.\)
\(\Rightarrow\left[{}\begin{matrix}x-5=3+x\\x-5=-3-x\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-x=3+5\\x+x=-3+5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}0=8\\2x=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x\in\varnothing\\x=2:2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x\in\varnothing\\x=1\end{matrix}\right.\)
Vậy \(x=1.\)
Chúc bạn học tốt!
Ta có :
\(\left|x-5\right|-x=3\)
\(\Leftrightarrow\left|x-5\right|=x+3\)
Lại có : \(\left|x-5\right|\ge0\forall x\)
\(\Leftrightarrow x+3\ge0\Leftrightarrow x\ge-3\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=x+3\\x-5=-x-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-x=5+3\\x+x=-3+5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}0x=8\left(vôli\right)\\2x=2\end{matrix}\right.\)
\(\Leftrightarrow x=1\left(tm\right)\)
Vậy.....
