Final answer:
After the collapse of Roman authority in western Europe, people faced challenges such as political fragmentation, invasions, economic instability, and social disarray.
Step-by-step explanation:
After the collapse of Roman authority in western Europe, people faced several challenges including political fragmentation, invasions, economic instability, and social disarray. With no centralized power, Europe experienced political and military discord, leading to the retreat of people into walled cities for protection against marauding pillagers. Travel became difficult and dangerous, harming commerce. Overall, the collapse of Roman authority had a significant impact on the people of western Europe.