\(N=\left|x-1004\right|+\left|x+1003\right|=\left|1004-x\right|+\left|x+1003\right|\le\left|1004-x+x+1003\right|=2007\)
Dấu "=" xảy ra khi \(\left(1004-x\right)\left(x+1003\right)\ge0\Leftrightarrow-1003\le x\le1004\)
Vậy MaxN = 2007 khi \(-1003\le x\le2004\)
N = |1004-x|+|x+1003| >= |1004-x+x+1003| = 2007
Dấu "=" xảy ra <=> (1004-x).(x+1003) >= 0
<=> -1003 <= x <= 1004
Vậy Min N = 2007 <=> -1003 <= x <= 1004