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

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The discussion centers on determining limits for variable 'a' based solely on the inequalities involving 'p' and 'q'. User Natski questions whether any constraints can be established for 'a' given the inequalities a + b > p and b > q. Another participant suggests visualizing the problem by graphing the inequalities x + y > p and y > q, indicating that the bounds for 'x' are influenced by 'y'. This graphical approach reveals the interdependence of the variables in the inequalities.

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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].
 

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