Question

用区间表示I={x|1<|x-2|<3}的实数集合，求过程

Answer 1

① x-2>1,x-2<-1 → x>3,x<1
② -3<x-2<3 → -1<x<5
⇒(-1,1)∪(3,5)

Answer 2

{x|1<|x-2|<3}
={x|-3<x-2<-1}U{x|1<x-2<3}
={x|-1<x<1}U{x|3<x<5}
=(-1,1)U(3,5)