Question

|2x-3|<5
|x-2|>1

I need answer for this inequalities

Answer 1

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,∞)