  We say that a group has property $R_{\infty}$ if any group automorphism has
an infinite number of twisted conjugacy classes. Fel'shtyn and Goncalves prove
that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{\infty}$.
We define a solvable generalization $\Gamma(S)$ of these groups which we show
to have property $R_{\infty}$. We then show that property $R_{\infty}$ is
geometric for these groups, that is, any group quasi-isometric to $\Gamma(S)$
has property $R_{\infty}$ as well.
