We report a measurement of the energy-dependent total charged-current cross section σ(Eν) for inclusive muon neutrinos scattering on argon, as well as measurements of flux-averaged differential cross sections as a function of muon energy and hadronic energy transfer (ν). Data corresponding to 5.3×1019 protons on target of exposure were collected using the MicroBooNE liquid argon time projection chamber located in the Fermilab booster neutrino beam with a mean neutrino energy of approximately 0.8 GeV. The mapping between the true neutrino energy Eν and reconstructed neutrino energy Eνrec and between the energy transfer ν and reconstructed hadronic energy Ehadrec are validated by comparing the data and Monte Carlo (MC) predictions. In particular, the modeling of the missing hadronic energy and its associated uncertainties are verified by a new method that compares the Ehadrec distributions between data and a MC prediction after constraining the reconstructed muon kinematic distributions, energy, and polar angle to those of data. The success of this validation gives confidence that the missing energy in the MicroBooNE detector is well modeled and underpins first-time measurements of both the total cross section σ(Eν) and the differential cross section dσ/dν on argon.