You are absolutely correct. I went to an inner city high school, Muskegon High School in Muskegon Michigan. The elementary schools on the city's west side were predominantly white whereas the rest of the city was mixed. The same pattern occurred at the junior high level with one on the west side mostly white and the other two mixed. But all schools fed a single high school, which was great. I graduated in 1978, but by the early 2000s with white families moving to the suburbs, the city shool population not only decreased but became majority black.