This paper proposes two variants of inertial algorithms designed to solve equilibrium problems in real Hilbert spaces, without assuming any generalized monotonicity or the Lipschitz-type condition of the bifunctions defining the problems. Our strategy replaces the shrinking projection step commonly used in existing algorithms with a projection onto a set defined by the feasible region and an appropriate half-space. Under the same assumptions for solving such problems, we show that the sequences generated by the proposed algorithms converge weakly and strongly to a solution of the equilibrium problem, respectively. Furthermore, some numerical examples are included to illustrate the effectiveness of the proposed algorithms.