=>2013= |x-4+10-x+x+101+999-x+x+1000|

rồi cộng lại đc bn + x

rồi chia Th ra

Xét VP = \(\left(\left|x-4\right|+\left|x+999\right|\right)+\left(\left|x-10\right|+\left|x+1000\right|\right)+\left|x+101\right|\)

\(\ge\left|x+999+4-x\right|+\left|x+1000+10-x\right|+\left|x+101\right|\)

\(=2013+\left|x+101\right|\ge2013=VT\)

=> VP \(\ge\)VT

Dấu "=" xảy ra <=>\(\hept{\begin{cases}\left(x+999\right)\left(4-x\right)\ge0\\\left(x+1000\right)\left(10-x\right)\ge0\\x+101=0\end{cases}}\)<=> x = -101

Vậy VP = VT <=> x = -101

x-14+x+2000

tick nhé

Ta co /x-4/+/x-10/+/x+101/+/x+990/+/x+1000/= /x+101/+/x-4/+/x-10/+/x+990/+/x+1000/= /x+101/+/x-4/+/x-10/+/x+990/+/x+1000/

>= /x+101/+/x-4+x-10+x+990+x+1000/=/x+101/+2013

=> 2013>=/x+101/+2013=.> /x+101/=<0

ma /x+101/>=0nen/x+101/=0=.>x=-101

Sai rồi bạn ơi

2004=(x-x-x+x+x)+(4+10+101+990+1000)

còn tiếp theo thì mk ko biết

Ta có: 

\(\left|x-4\right|+\left|x-10\right|+\left|x+101\right|+\left|990\right|+\left|x+1000\right|\)

\(=\left|x+101\right|+\left|x-4\right|+\left|x-10\right|+\left|x+990\right|+\left|x+1000\right|\)

\(\ge\left|x+101\right|+\left|x-4+x-10+x+990+x+1000\right|x+101\left|+\right|2004\)

\(\Rightarrow2004\ge\left|x+101\right|+2004\Rightarrow\left|x+101\right|\le0\)

Mà: \(\left|x+101\right|\ge0\)nên \(\left|x+101\right|=0\Rightarrow x=-101\)

Vậy: \(x=-101\)