Question: How to multiply an inequality by a name

Multiplication is possible by a numerical constant

a < b;
-1*%;
                             a < b

                            -b < -a

However, using a name with assumptions

with(RealDomain):# just to make sure that a and b are real, probably not required
ineq := a/c < b/c;
assume(c < 0);
c*ineq;
expand(%);
eval(%);
                                 a   b
                         ineq := - < -
                                 c   c

                           /a   b   \
                          *|- < -, c|
                           \c   c   /

                           /a   b   \
                          *|- < -, c|
                           \c   c   /

                           /a   b   \
                          *|- < -, c|
                           \c   c   /

does not work. Have I missed an essential assumption/trick?

What else can I do?

Or: is there a mathematical reasons not to offer this possibilty.

Context: For manual case studies of parameters in inequalties I find it sometimes helpfull to remove rational expressions. Doing this manually with lhs/rhs and denom and flipping < or > is prone to errors

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