There is an undocumented user-contributed feature of Maxima for rational inequalities: solve_rat_ineq().
Here are few examples of its capabilities and limitations:
There is an undocumented user-contributed feature of Maxima for rational inequalities: solve_rat_ineq().
Here are few examples of its capabilities and limitations:
The MaximaList 
For *systems* of inequalities, you can use **fourier_elim** in the **to_poly_solve** package:
(%i1) load(to_poly_solve)$
WARNING: redefining MAXIMA::OPAPPLY in DEFMACRO
WARNING: redefining MAXIMA::OPCONS in DEFMACRO
(%i2) fourier_elim( [ a+b > 0, a*b < 0 ], [a,b] );
(%o2) [- b < a, a < 0, 0 < b] or [- b < a, b 0, a*b < 0, a = 2 ], [a,b] );
(%o3) [a = 2, – 2 < b, b < 0]
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