|x + 3| + |x + 5| + |x + 7| = 4x + 1
Có: \(\left\{{}\begin{matrix}\left|x+3\right|>0\\\left|x+5\right|>0\\\left|x+7\right|>0\end{matrix}\right.\) \(\forall x\)
Do đó, \(4x+1>0=>4x>1=>x>\frac{1}{4}\)
Lúc này ta có: \(\left(x+3\right)+\left(x+5\right)+\left(x+7\right)=4x+1\)
=> \(3x+15=4x+1\)
=> \(15-1=4x-3x\)
=> \(14=1x\)
=> \(x=14:1\)
=> \(x=14\).
Vậy \(x=14\).
Chúc bạn học tốt!
\(\left|x+3\right|+\left|x+5\right|+\left|x+7\right|=4x+1\)
=> \(\left|x+3+x+5+x+7\right|=4x+1\)
=> \(\left|3x+15\right|=4x+1\)
=>\(\left[{}\begin{matrix}3x+15=4x+1\\3x+15=4x-1\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}4x-3x=15-1\\4x-3x=15+1\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=14\\x=16\end{matrix}\right.\)
Vậy \(x\in\left\{14;16\right\}\)
