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Longitudinal ($R_L$) and transverse ($R_T$) responses from inclusive electron scattering from carbon 12 and calcium 40 nuclei are computed within a fully relativistic and unfactorized model for the initial and final states, and one- and two-body current operators leading to the one-particle one-hole responses. We find that the two-body contributions have no effect on $R_L$ but they increase $R_T$ by up to 30%, depending on the energy and momentum transfer. Inclusive cross sections have also been computed. In this case, the increase of $R_T$ due to two-body currents will translate into an increase in the cross-sections depending on the degree of transversity of each kinematic. The comparison with carbon data is good for the responses and the cross sections. In the case of calcium, while the model compares well with the cross section data, the agreement with the responses is generally poor. However, the inconsistencies between different data sets for the separate responses in this nucleus points to uncertainties underlying the procedure to extract the responses that are not considered (or largely underestimated) in the experimental error bars. Our calculation is fully relativistic and considers within the full quantum mechanical description both the initial and final nucleon states involved in the process. We also show that it is essential to go beyond the plane-wave approach, since incorporating the distortion of the nucleons while making the initial and final states orthogonal, allows to reproduce both the shape and magnitude of the cross section data and carbon responses. The good agreement with the electron scattering experimental data supports the use of this approach to describe the analogous neutrino-induced scattering reaction.