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Over ∼150 resolved, kpc-scale X-ray jets hosted by active galactic nuclei have been discovered with the Chandra X-ray Observatory. A significant fraction of these jets have an X-ray spectrum either too high in flux or too hard to be consistent with the high-energy extension of the radio-to-optical synchrotron spectrum, a subtype we identify as Multiple Spectral Component (MSC) X-ray jets. A leading hypothesis for the origin of the X-rays is the inverse-Compton scattering of the cosmic microwave background by the same electron population producing the radio-to-optical synchrotron spectrum (known as the IC/CMB model). In this work, we test the IC/CMB model in 45 extragalactic X-ray jets using observations from the Fermi Large Area Telescope to look for the expected high level of gamma-ray emission, utilizing observations from the Atacama Large Millimeter/submillimeter Array (ALMA) and the Hubble Space Telescope (HST) when possible to best constrain the predicted gamma-ray flux. Including this and previous works, we now find the IC/CMB model to be ruled out in a total of 24/45 MSC X-ray jets due to its over-prediction for the observed MeV-to-GeV gamma-ray flux. We present additional evidence against the IC/CMB model, including the relative X-ray-to-radio relativistic beaming in these sources, and the general mismatch between radio and X-ray spectral indexes. Finally, we present upper limits on the large-scale bulk-flow Lorentz factors for all jets based on the Fermi upper limits, which suggest that these jets are at most mildly relativistic. [ABSTRACT FROM AUTHOR]