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Simultaneous inequalities

  1. Aug 31, 2011 #1
    Hi all,


    a + b > p
    b > q

    Is there no way to place any limits on a in terms of p and q only? I know that one is allowed to add inequalities together but not subtract, but is there any other tricks one can play to solve this?

  2. jcsd
  3. Aug 31, 2011 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    I find it easier to think of the problem as
    [itex] x + y > p [/itex]
    [itex] y > q [/itex]

    If you graph the area on the xy plane that contains points (x,y) that satisfy the inequalities, I think you can see that the upper and lower bounds for x are dependent on y. For example, try graphing the solution of [itex] x + y > 1 [/itex] and [itex] y > 3 [/itex].
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