Vehicle-to-everything (V2X) communication and services have been garnering significant interest from different stakeholders as part of future intelligent transportation systems (ITSs). This is due to the many benefits they offer. However, many of these services have stringent performance requirements, particularly in terms of the delay/latency. Multi-access/mobile edge computing (MEC) has been proposed as a potential solution for such services by bringing them closer to vehicles. Yet, this introduces a new set of challenges such as where to place these V2X services, especially given the limit computation resources available at edge nodes. To that end, this work formulates the problem of optimal V2X service placement (OVSP) in a hybrid core/edge environment as a binary integer linear programming problem. To the best of our knowledge, no previous work considered the V2X service placement problem while taking into consideration the computational resource availability at the nodes. Moreover, a low-complexity greedy-based heuristic algorithm named "Greedy V2X Service Placement Algorithm" (G-VSPA) was developed to solve this problem. Simulation results show that the OVSP model successfully guarantees and maintains the QoS requirements of all the different V2X services. Additionally, it is observed that the proposed G-VSPA algorithm achieves close to optimal performance while having lower complexity. 1) Communication Modes: To cover all possible on-road interactions, the 3GPP project proposed four different communication modes. This includes vehicle-to-network (V2N), vehicle-to-infrastructure (V2I), vehicle-to-vehicle (V2V), and vehicle-to-pedestrian (V2P) communication [5] as shown in Fig. 2. Depending on the service or application, a communication mode can be chosen. A brief overview of each of these communication modes is provided below: a-V2N Communication: V2N communication refers to the communication between a vehicle and a V2X application server. This is typically done using a cellular network such as an LTE network [9], [10]. Through this connection, different services such as infotainment, traffic optimization, navigation, and safety can be offered [11], [12].