Simultaneous inequalities

1. Aug 31, 2011

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

2. Aug 31, 2011

Stephen Tashi

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 $y > 3$.