\(\left|x+\frac{11}{67}\right|+\left|x+\frac{2}{17}\right|+\left|x+\frac{4}{17}\right|=4x\)
Có: \(\left\{{}\begin{matrix}\left|x+\frac{11}{67}\right|\\\left|x+\frac{2}{17}\right|\\\left|x+\frac{4}{17}\right|\end{matrix}\right.>0\forall x.\)
Do đó \(4x>0\Rightarrow x>0.\)
Lúc này ta có: \(\left(x+\frac{11}{67}\right)+\left(x+\frac{2}{17}\right)+\left(x+\frac{4}{17}\right)=4x\)
⇒ \(\left(x+x+x\right)+\left(\frac{11}{67}+\frac{2}{17}+\frac{4}{17}\right)=4x\)
⇒ \(3x+\frac{589}{1139}=4x\)
⇒ \(4x-3x=\frac{589}{1139}\)
⇒ \(1x=\frac{589}{1139}\)
⇒ \(x=\frac{589}{1139}:1\)
⇒ \(x=\frac{589}{1139}\left(TM\right)\)
Vậy \(x=\frac{589}{1139}.\)
Chúc bạn học tốt!