Ta có:
|x+1| + |x+2| +....+ |x+100|=605x
x+1+x+2+x+3+.....+x+100=605x
x+x+x+x+..+x+1+2+3+.....+100=605x
100x+(100+101/2)=605x
100x+5050=605x
5050=605x-100x
5050=505x
x=5050:505
x=10
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\(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+.....+\left|x+100\right|=605x\)
\(\left|x+1\right|\ge0;\left|x+2\right|\ge0;\left|x+3\right|\ge0;......\left|x+100\right|\ge0\)
\(\Rightarrow\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+.....+\left|x+100\right|\ge0\)
\(\Rightarrow x+1+x+2+x+3+.....+x+100=605x\)
\(100x+\left(1+2+3+.....+100\right)=605x\)
\(1+2+3+.....+100=505x\)
\(\left[\left(\dfrac{100-1}{1}+1\right):2\right]\left(100+1\right)=50.101=5050=505x\)\(x=5050:505=10\)
