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## Homework Statement

What are the possible values of |2x−3| when 0<|x−1|<2?

## Homework Equations

## The Attempt at a Solution

We know [itex]\left|x-1\right|[/itex] becomes x-1 if x-1≥0 and -(x-1) if x-1<0.

Now consider two cases.

Case 1:

0<x-1<2 [itex]\Rightarrow[/itex] 1<x<3 [itex]\Rightarrow[/itex] -1<2x-3<3.

Case 2:

0<-x+1<2 [itex]\Rightarrow[/itex] -1<x<1 [itex]\Rightarrow[/itex] -2<2x<2 [itex]\Rightarrow[/itex] -5<2x-3<-1.

Then the possible value include -1<|2x-3|<3 and -5<|2x-3|<-1.

Am I going about this problem correctly?