Can Limits on Variable a Be Determined Solely by p and q?

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natski
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Hi all,

Given...

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?

Thanks,
Natski
 
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natski said:
Is there no way to place any limits on a in terms of p and q only?

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].