Is there a known important class of $\mathbb{Z} $-linear reidually solvable groups, except for free groups?

It is just a rough question and I'm not an expert on this subject. I read some books on polycyclic groups and saw two theorems: solvable $\mathbb{Z}$-linear groups are polycyclic, and a polycyclic group is residually nilpotent-by-finite. We can also easily deduce that a residually f.g. nilpotent group is residually polycyclic.

Now I have a question: are $\mathbb{Z}$-linear residually (f.g.-)solvable groups residually polycyclic? But this question may not be interesting at all, from some triviality I don't know. Anyone help?


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