Giải:
\(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|=5x\)
\(\ge\left|x+1+x+2+x+3+x+4\right|=5x\)
\("="\Leftrightarrow\left|4x+10\right|=5x\)
\(\Leftrightarrow\left[{}\begin{matrix}4x+10=5x\\4x+10=-5x\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=10\left(n\right)\\x=-\dfrac{10}{9}\left(l\right)\end{matrix}\right.\)
Vậy ...
Ta có
\(\left|x+1\right|\ge0\)
\(\left|x+2\right|\ge0\)
\(\left|x+3\right|\ge0\)
\(\left|x+4\right|\ge0\)
=> \(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|\ge0\)
=> 5x\(\ge0\)
Dấu "=" xảy ra <=>
x+1+x+2+x+3+x+4=5x
=> (x+x+x+x)+(1+2+3+4)=5x
=> 4x+10=5x
=> 5x-4x=10
=> x=10
Vậy x=10
cô giáo mk dạy vậy đó , nên chắc chắn là đúng
