求不等式的整数解{y-│x-3│+1/2>0 y+│x-1│<=2

y-|x-3|+1/2>0
y+|x-1|<=2
|x-3|-1/2<y<=2-|x-1|

|x-3|-1/2<2-|x-1|
若x>=3
x-3-1/2<2-x+1
x-3.5<3-x
2x<6.5
x<3.25
3<=x<3.25
所以x=3
-1/2<y<=0
y=0
{x=3,y=0

若1<=x<3
3-x-0.5<2-x+1
2.5-x<3-x
此时2.5<y<3
无整数解

当x<1
3-x-0.5<2-1+x
2.5-x<1+x
1.5<2x
x>0.75
所以0.75<x<1无整数解

因此只有一组整数解x=3,y=0