Finitely generated and solvable not implies finitely presented

Statement
There exists a finitely generated solvable group (i.e., a group that is both finitely generated and solvable) that is not finitely presented, i.e., it has no presentation with finitely many generators and finitely many relations.

Similar facts

 * Stronger than::Finitely generated not implies finitely presented
 * Stronger than::Noetherian not implies finitely presented: A Noetherian group (also called snder group) is a group in which every subgroup is finitely generated. Such a group need not be finitely presented.

Opposite facts

 * Polycyclic implies finitely presented: A polycyclic group can be defined as a Noetherian solvable group. It turns out that any polycyclic group is finitely presented.
 * Finitely generated abelian implies finitely presented (via polycyclic)
 * Finitely generated nilpotent implies finitely presented (via polycyclic)