\( \left|x+5\right|+\left|2-3x\right|=5x\)
\(\left\{{}\begin{matrix}\left|x+5\right|\ge0\forall x\\\left|2-3x\right|\ge0\forall x\end{matrix}\right.\)
\(\Rightarrow\left|x+5\right|+\left|2-3x\right|\ge0\)
\(\Rightarrow5x\ge0\)
\(\Rightarrow x+5+2-3x=5x\)
\(\Rightarrow-2x+7=5x\)
\(\Rightarrow7x=7\)
\(\Rightarrow x=1\)
- Xét:
+ x < 0 => x vô ngiệm ( vì khi x = 0 => vế trái \(\ge\)0 , vế phải <0)
- Xét x\(\ge\) 0
=> \(\left\{{}\begin{matrix}5+x=0\\2x-3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-5\\y=\dfrac{3}{2}\end{matrix}\right.\)
- Vậy x=-5 ; y=\(\dfrac{3}{2}\)
