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,∞)
