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Math Help - Inequalities

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    1

    Inequalities

    Hi There,

    Just something i wanted to clarify.

    I have the equation:

    a * b <= b

    Which answer is correct?

    1)

    a >= b/b
    a>=1
    a > 0

    or

    2)

    a <= b/b
    a <= 1
    a < 2

    Its just that in answer one i cant remember if you flip the inequality sign because you are bringing the b over to the other side and dividing.
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  2. #2
    Newbie
    Joined
    Nov 2008
    Posts
    6
    It's the second one. You only switch the sign if you divide by a negative number.

    Bo

    Although I'm not sure why you'd finish it with <2. Can you not just leave your answer as a<=1
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  3. #3
    Senior Member
    Joined
    Nov 2007
    Posts
    329
    1*5=<5 so 1=<1
    2*(-5)=<-5 so 2=<1 which is not true.
    So if you divide by a negative number then switch the sign (and don't divide by 0). So the thing is depending on b. If you don't know anything about it then you should do the cases b>0, b<0 and b=0 separately.
    So the solution to the inequality a\cdot b\le b is b<0\quad a\ge 1 and b>0\quad a\le 1 and b=0\quad \forall a\in\mathbb{R}.
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