Example of racial injustice that king uses support for his claim that african americans are not free

Segregation. It's "separate but equal" idea did not ring true in all places. Black children went to poorer schools, where they recieved inadequate education and supplies. Black communities were purposely lower-quality, with broken-down buildings.

Voting. Few blacks were allowed to vote, and even then you had to go through an approval system. The moderators/courts would always decline blacks and admit whites, despite their education.