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Tongzhou Grade Three, 20 17, One Model of Mathematics
| x-1|+x-2018 |≥| 2018-1| = 2017 if and only if1≤ x ≤ 20/kloc-.

Similarly,

| x-2 |+| x-2017 |≥| 2017-2 | = 2015 is an equal sign if and only if 2≤x≤20 17.

…………

| x-1008 || x-1009 |≥|101008 | = 2 if and only if1008 ≤ x ≤/.

|x- 1009|≥0, if and only if x= 1009, take the equal sign.

If and only if x= 1009, | x-1| x-2018 |, | x-2 ||| x-2017 |, ..., | x-/kloc-0.

|x- 1|+|x-2|+|x-3|+...+|x-20 18|≥0+2+...+20 17

=2( 1+2+...+ 1008)

= 10 17072