  The hybrid model for electroweak single-pion production (SPP) off the
nucleon, presented in [Gonz\'alez-Jim\'enez et al., Phys. Rev. D 95, 113007
(2017)], is extended here to the case of incoherent pion-production on the
nucleus. Combining a low-energy model with a Regge approach, this model
provides valid predictions in the entire energy region of interest for current
and future accelerator-based neutrino-oscillation experiments. The Relativistic
Mean-Field model is used for the description of the bound nucleons while the
outgoing hadrons are considered as plane waves. This approach, known as
Relativistic Plane-Wave Impulse Approximation (RPWIA), is a first step towards
the development of more sophisticated models, it is also a test of our current
understanding of the elementary reaction. We focus on the charged-current
$\nu$($\bar\nu$)-nucleus interaction at MiniBooNE and MINERvA kinematics. The
effect on the cross sections of the final-state interactions, which affect the
outgoing hadrons on their way out of the nucleus, is judged by comparing our
results with those from the NuWro Monte Carlo event generator. We find that the
hybrid-RPWIA predictions largely underestimate the MiniBooNE data. In the case
of MINERvA, our results fall below the $\nu$-induced 1$\pi^0$ production data,
while a better agreement is found for $\nu$-induced 1$\pi^+$ and
$\bar\nu$-induced 1$\pi^0$ production.
