Using known results regarding PCP,
we present simple proofs of the inapproximability
of vertex cover for hypergraphs.
Specifically, we show that

(1) Approximating the size of the minimum vertex cover
in $O(1)$-regular hypergraphs to within a factor of~1.99999 is NP-hard.
(2) Approximating the size of the minimum vertex cover
in $4$-regular hypergraphs to within a factor of~1.49999 is NP-hard.

Both results are inferior to known results (by Trevisan and Holmerin),
but they are derived using much simpler proofs.
Furthermore, these proofs demonstrate the applicability
of the FGLSS-reduction in the context of reductions among
combinatorial optimization problems.