Question

解不等式: |x-3| - |2x+1| <2

Answer 1

解：分类讨论：
当x<-1/2时
3-x+(2x+1)<2
即x<-2
所以x<-2

当-1/2≤x≤3时
3-x-(2x+1)<2
即x>0
所以0<x≤3

当x>3时
x-3-(2x+1)<2
即x>-6
所以x>3

综上，x<-2或x>0

Answer 2

x<-1/2
则x-3<0,2x+1<0
3-x-(-2x-1)<2
3-x+2x+1<2
x<0
所以x<-1/2

-1/2<=x<=3
则x-3<=0,2x+1>=0
3-x-(2x+1)<2
3-x-2x-1<2
x>0
所以0<x<=3

x>3
则x-3>0,2x+1>0
x-3-(2x+1)<2
x-3-2x-1<2
x>-6
所以x>3

所以
x<-1/2，x>0