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Possible Values of the Inequality.

  1. Sep 28, 2013 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations



    3. 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?
     
  2. jcsd
  3. Sep 28, 2013 #2

    Office_Shredder

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    Saying -5< |2x-3| is not a particularly bold statement to make.... take another look at the inequalities you got before you took the absolute value and think a bit harder about what they tell you about the absolute value.
     
  4. Sep 28, 2013 #3
    Then the possible solutions should probably just be |2x-3|<3, since no solution exists to the inequality -5<|2x-3|<-1 since |2x-3| is bounded by negative values.
    Am I right?
     
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