Summary: We show that for any finitely generated solvable group of exponential growth one can find a measure-preserving action for which the multiple recurrence theorem fails and a measure-preserving action for which the ergodic Roth theorem fails. This is in contrast with the positive results established by A. Leibman [Geom. Funct. Anal. 8, No. 5, 853–931 (1998; Zbl 0917.28017)] and V. Bergelson and A. Leibman [Invent. Math. 147, No. 2, 429–470 (2002; Zbl 1042.37001)] for nilpotent group actions.