We propose a projective splitting type method to solve the problem of finding a zero of the sum of two maximal monotone operators. Our method considers inertial and relaxation steps, and also allows inexact solutions of the proximal subproblems within a relative-error criterion.We study the asymptotic convergence of the method, as well as its iteration-complexity. We also discuss how the inexact computations of the proximal subproblems can be carried out when the operators are Lipschitz continuous. In addition, we provide numerical experiments comparing the computational performance of our method with previous (inertial and non-inertial) projective splitting methods.