Just to explain what might be a tricky point, an equation like F = ma isn't just pulled out of the aether. It's a representation of known and studied behavior.
There is no known and studied behavior of objects with negative mass. There isn't even a rationale for throwing down absolute-value bars beyond "symmetry".
There is no known and studied behavior of objects with negative mass. There isn't even a rationale for throwing down absolute-value bars beyond "symmetry".