<p>We propose a relaxed inertial-Tseng method for solving monotone inclusion problem in a real Hilbert. The newly proposed inertial condition is relaxed and easy to implement, and its upper bound is easy to obtain unlike many conditions in the literature. We obtain a weak convergence result of the proposed method under weaker conditions and we present a series of numerical computations involving our newly suggested method, compared with established methods in the literature. In addition, the theoretical result is applied to image restoration problems. Notably, our findings enhance, broaden, and advance various preexisting outcomes available in scholarly discourse.</p>