Solution of linear inequalityI have the following system of linear inequality on x 1 , x 2 , … , x n , x i ∈ R ∀ i x i − 2 x j &lt; b ∀ i , j The right hand side of the inequality ( b ∈ R + ) is fixed (and given) for all inequalities.From simulation I can see that the only solution to this system of equation is when all x i 's are equal. Is there a formal proof to show this ?

Question

Solution of linear inequalityI have the following system of linear inequality on       x    1    ,      x    2    ,  …  ,      x    n  ,       x    i    ∈  R    ∀  i      x    i    −  2      x    j    &amp;lt;  b    ∀  i  ,  j The right hand side of the inequality (  b  ∈        R    +  ) is fixed (and given) for all inequalities.From simulation I can see that the only solution to this system of equation is when all       x    i  &#039;s are equal. Is there a formal proof to show this ?

Elias Flores · Accepted Answer

You need to have some restriction on   b.Otherwise, for any set of       x    i  , choose   b  &amp;gt;  3  max  (  |      x    i    |  ). Then all the inequalities hold.