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Possible Values of the Inequality.

  • Thread starter NATURE.M
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  • #1
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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?
 

Answers and Replies

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