奧數問題..急!!!---|x-2|+|x+3|>5

1 | | 是將負數變成正數的符號。如 |-3| = |3| = 3

2 |x - 2| + |x + 3| > 5

若x < -3, 原式變成

(2 - x) - (x + 3) > 5

-2x - 1 > 5

x < -3

若 -3 <= x <= 2, 原式變成

(2 - x) + (x + 3) > 5

5 > 5

矛盾

若x > 2,原式變成

(x - 2) + (x + 3) > 5

2x + 1 > 5

x > 2

因此滿足|x - 2| + |x + 3| > 5的所有整數x的和

= (-4) + (-5) + ... + 3 + 4 + 5 + ...

= 3 (抵消後)

or absolute value:
e.g.
I a I = 10
a = 10 or -10

Meaning of " | " :

If a = b or -b, which b>0,

then |a| = b