The ArgoNeuT collaboration presents measurements of inclusive muon neutrino and antineutrino charged current differential cross sections on argon in the Fermilab NuMI beam operating in the low energy antineutrino mode. The results are reported in terms of outgoing muon angle and momentum at a mean neutrino energy of 9.6 GeV (neutrinos) and 3.6 GeV (antineutrinos), in the range $0^\circ < \theta_\mu < 36^\circ$ and $0 < p_\mu < 25$ GeV/$c$, for both neutrinos and antineutrinos.