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

[natski]

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

 

[Stephen Tashi]

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
$x + y > p$
$y > q$

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 $x + y > 1$ and $y > 3$.