Đặt [tex]A=\left | x+1 \right |+\left | x+2 \right |+...+\left | x+2017 \right |[/tex]
Có: [tex]A\geq 0[/tex] ( với mọi x thuộc R)
mà A=2018x => 2018x >= 0 <=> x>=0
=> A= x+1+x+2+...+x+2017=2018x
<=> 2017x +(1+2+3+...+2017)=2018x
<=> 2017x+ 2035153=2018x
<=> x= -2035153