How to solve inequalities with parallel processing?

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You can try defining the polytope of the set of points satisfying all inequalities. For this, you can have a look at the Polyhedron constructor as follows:

sage: Polyhedron?

If P is the polyhedron you constructed, you can try to find an element with the .an_element() method.

You can have a look at the backend option for the Polyhedron constructor, there is cdd, normaliz, polymake, ppl, so perhaps one of them implements parallel algorithms (however, it is likely that without parallelism, those backends will be faster than the symbolic solver behind solve_ineq).

Do not hesitate to ask from more details by explaining what you tried so far.