Very Nice Algebra Challenge | Math Olympiad Problem📌

[@KipIngram]

x = 5.5 is one solution, by inspection. This works because 6-5.5 and 7-5.5 are the negatives of 5-5.5 and 4-5.5. There should actually be two other solutions, though. We can multiply the original equation through by all of these denominators, and the result will be a cubic equation in x, which should have three solutions in the complex plane. I'm feeling too lazy to do all that algebra right now, though.