Find greatest and smallest solution of an inequalities system

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I need to create an algorithm that automatically solves an inequalities system similar to this:
V = v0 + v1*x
A = a0 + a1*x + a2*x^2
J = j0 + j1*x + j2*x^2 + j3*x^3
0 <= V <= F
-Amax <= A <= Amax
-Jmax <= J <= Jmax
What i really need is to find the biggest and the lowest solution of this system.
Since this has to be done thousands of times I need this to be totally automatic.
My problematics are:
- solve( V<=F, x ) returns something like "Dom::Interval(-inf, [3/10])", which is an interval, but I can't deal with it because in reality it is a "sym 1x1"
- How can I manage intervals without entering the MuPAD environment?
- How can I find the greatest and the lowest and the smallest value of this interval without entering the MuPAD environment?

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