  Inflection-point inflation is an interesting possibility to realize a
successful slow-roll inflation when inflation is driven by a single scalar
field with its value during inflation below the Planck mass ($\phi_I \lesssim
M_{Pl}$). In order for a renormalization group (RG) improved effective $\lambda
\phi^4$ potential to develop an inflection-point, the running quartic coupling
$\lambda(\phi)$ must exhibit a minimum with an almost vanishing value in its RG
evolution, namely $\lambda(\phi_I) \simeq 0$ and $\beta_{\lambda}(\phi_I)
\simeq 0$, where $\beta_{\lambda}$ is the beta-function of the quartic
coupling. In this paper, we consider the inflection-point inflation in the
context of the minimal gauged U(1)$_X$ extended Standard Model (SM), which is a
generalization of the minimal U(1)$_{B-L}$ model, and is constructed as a
linear combination of the SM U(1)$_Y$ and U(1)$_{B-L}$ gauge symmetries. We
identify the U(1)$_X$ Higgs field with the inflaton field. For a successful
inflection-point inflation to be consistent with the current cosmological
observations, the mass ratios among the U(1)$_X$ gauge boson, the right-handed
neutrinos and the U(1)$_X$ Higgs boson are fixed. Focusing on the case that the
extra U(1)$_X$ gauge symmetry is mostly aligned along the SM U(1)$_Y$
direction, we investigate a consistency between the inflationary predictions
and the latest LHC Run-2 results on the search for a narrow resonance with the
di-lepton final state. %In addition, the inflection-point inflation provides a
unique prediction for the running of the spectral index $\alpha \simeq - 2.7
\times %10^{-3}\left(\frac{60}{N}\right)^2$ ($N$ is the e-folding number),
which can be tested in the near future.
