A city of 50,000 or more inhabitants, or an urbanized area of at least 50,000 inhabitants, with adjacent communities having a high degree of economic and social integration with the core community is called a:

metropolitan statistical area

Explanation:

Based on the information provided within the question it can be said that term that is being described is known as a metropolitan statistical area (MSA). This is a region that contains a city and various communities which are all linked by social and economic factors and is a  term was created by the  U.S. Office of Management and Budget

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