1). x<0sud21 wrote:Is |x-2|+|x+2|<4?
1). x<0
2). x is within (-2, 2)
Case 1:
-2<x<0
|-1-2|+|-1+2| = 3+1 = 4
Is |x-2|+|x+2|<4?
No
Case 2:
x = -2
|-2-2|+|-2+2| = 4
Is |x-2|+|x+2|<4?
No
Case 3:
x < -2
|-3-2|+|-3+2|= 5+1 = 6
Is |x-2|+|x+2|<4?
No
Sufficient
2). x is within (-2, 2)
this means
-2<x<2
(x-2) is negative
|x-2| = 2-x
|x+2| = x+2
|x-2|+|x+2| = 2-x + x+2 = 4
Is |x-2|+|x+2|<4?
No
Suff
Option D
