|2x-3|< 5 |x-2|> 1 i need answer for this inequalities

1)first step

for the first  inequation you need apply  the following property,  IXI < a

-a<x<a, them  you must substitute  2x-3, of this form

-5<2x-3<5⇒ -5+3<2x-3+3<5+3⇒-2<2x<8⇒-2/2<2x/2<8/2⇒  -1<x<4,

the solution is

S1 =(-1,4)

2) For the second inequality  apply the following  property

IXI>a ,   x<-a or  x >a , therefore

IX-2I>1  ⇒X-2 <-1  OR  X-2> 1

X-2<-1⇒X-2+2<-1+2⇒ X< 1

OR

X-2>1⇒X>1+2⇒X>3

THE SOLUTION IS S2 = (-∞,1)∪(3,∞)

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.