Với mọi giá trị của \(x\in R\) ta có:
\(\left|x+1\right|\ge0;\left|x+1,2\right|\ge0;\left|x+1,3\right|\ge0;\left|x+1,4\right|\ge0\)
\(\Rightarrow\left|x+1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|\ge0\)
mà \(\left|x+1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|=5x\)
nên \(5x\ge0\Rightarrow x\ge0\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x+1\right|=x+1\\\left|x+1,2\right|=x+1,2\\\left|x+1,3\right|=x+1,3\\\left|x+1,4\right|=x+1,4\end{matrix}\right.\)
\(\Rightarrow x+1+x+1,2+x+1,3+x+1,4=5x\)
\(\Rightarrow4x+4,9=5x\Rightarrow x=4,9\)
Chúc bạn học tốt!!!
\(\left|x+1\right|\ge0\) \(\left|x+1,2\right|\ge0\)
\(\left|x+1,3\right|\ge0\) \(\left|x+1,4\right|\ge0\)
\(\Leftrightarrow\left|x+1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|\ge0\)
\(\Leftrightarrow x+1+x+1,2+x=1,3+x+1,4=5x\)
\(4x+4,9=5x\)
\(\Leftrightarrow x=4,9\)