Help me out with this (1/x)<x<1

  • Thread starter garyljc
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  • #1
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Main Question or Discussion Point

Hi all ,
could someone help me out with this
(1/x)<x<1

i tried by drawing the graphs
and separated it in 2 equations
but the answer that i found was -1<x<1
is it correct ?
 

Answers and Replies

  • #2
103
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i got a new breakthrough haha
this equation does not have a solution set

correct me if i'm wrong
if first do the first 2 steps of the equation ,it follows that 1/x < x
therefore x^2>1
second equation will be that x<1
therefore there is no solution
am i correct ?
 
  • #3
tiny-tim
Science Advisor
Homework Helper
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Hi garyljc! :smile:
1/x < x
therefore x^2>1

am i correct ?
Nope! :smile:

Hint: If a < b and c < 0, is ac < bc? :wink:
 
  • #4
25
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1/x<x
1/x - x<0
(1-x^2)/x<0
(x^2 - 1)/x>0

case 1: numerator and denominator are positive
numerator
x^2-1>0
(x+1)(x-1)>0
By wavy curve method
x<-1 or x>1
denominator
x>0
so solution for this case is x>1
but x<1 (given in the question)
hence no solution in this case.

case 2: numerator and denominator are negative
x^2-1<0
(x+1)(x-1)<0
By wavy curve method
-1<x<1
x<0
so solution for this case is -1<x<0
but x<1
hence solution for this case is -1<x<0

SO THE ANSWER IS -1<X<0
 
  • #5
103
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thanks to both lizzie and tim
 
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