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0

$begingroup$

If I have 3 variables, $x_1$, $x_2$, $x_3$ which can all take values between plus/minus infinity, what values of $x_1$ satisfy all conditions:

$x_2 > x_1 >x_3$

$x_2>0$

$x_3<0$

Any tips would be appreciated!

algebra-precalculus inequality

share|cite|improve this question

asked Mar 15 at 17:11

darren86darren86

567

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Which number you tried to take?
  $endgroup$
  – Michael Rozenberg
  Mar 15 at 17:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Does $x_1$ have to satisfy all inequalities, whatever the values of $x_2,x_3$ are?
  $endgroup$
  – Dr. Mathva
  Mar 15 at 18:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Dr.Mathva To clarify in words.....I'm looking for all values of $x_1$ such that it must be less than $x_2$ and greater than $x_3$, where $x_2 >0$ and $x_3 < 0$
  $endgroup$
  – darren86
  Mar 16 at 15:04
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Well, since $x_2 >0$ and $x_3 <0$, the interval $[x_3, x_2]$ is nonempty since it includes the value $0$. So the answer is simply the first condition, i.e. the values of $x_1$ which satisfy all three conditions are given by all $x_1$ with $x_2 > x_1 >x_3$.
  $endgroup$
  – Andreas
  Mar 16 at 18:04
  

  
  
  
  

add a comment | 

0

$begingroup$

If I have 3 variables, $x_1$, $x_2$, $x_3$ which can all take values between plus/minus infinity, what values of $x_1$ satisfy all conditions:

$x_2 > x_1 >x_3$

$x_2>0$

$x_3<0$

Any tips would be appreciated!

algebra-precalculus inequality

share|cite|improve this question

asked Mar 15 at 17:11

darren86darren86

567

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Which number you tried to take?
  $endgroup$
  – Michael Rozenberg
  Mar 15 at 17:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Does $x_1$ have to satisfy all inequalities, whatever the values of $x_2,x_3$ are?
  $endgroup$
  – Dr. Mathva
  Mar 15 at 18:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Dr.Mathva To clarify in words.....I'm looking for all values of $x_1$ such that it must be less than $x_2$ and greater than $x_3$, where $x_2 >0$ and $x_3 < 0$
  $endgroup$
  – darren86
  Mar 16 at 15:04
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Well, since $x_2 >0$ and $x_3 <0$, the interval $[x_3, x_2]$ is nonempty since it includes the value $0$. So the answer is simply the first condition, i.e. the values of $x_1$ which satisfy all three conditions are given by all $x_1$ with $x_2 > x_1 >x_3$.
  $endgroup$
  – Andreas
  Mar 16 at 18:04
  

  
  
  
  

add a comment | 

$begingroup$

If I have 3 variables, $x_1$, $x_2$, $x_3$ which can all take values between plus/minus infinity, what values of $x_1$ satisfy all conditions:

$x_2 > x_1 >x_3$

$x_2>0$

$x_3<0$

Any tips would be appreciated!

algebra-precalculus inequality

share|cite|improve this question

asked Mar 15 at 17:11

darren86darren86

567

$endgroup$

share|cite|improve this question

asked Mar 15 at 17:11

darren86darren86

567

share|cite|improve this question

asked Mar 15 at 17:11

darren86darren86

567

asked Mar 15 at 17:11

darren86darren86

567

asked Mar 15 at 17:11

darren86darren86

567