Final answer:
The Middle East country that took US hostages and contributed to a perception of weakness in President Carter's administration was Iran. The crisis began when Iranian students captured 52 American citizens at the US embassy in Tehran, demanding the return of the shah who was in the US. The hostages were held for 444 days, and their release coincided with the inauguration of Ronald Reagan.
Step-by-step explanation:
The Middle East country that took US hostages and made President Jimmy Carter appear weak was Iran. The hostages were seized on November 4, 1979, after Iranian students stormed the US embassy in Tehran, demanding the return of the shah, who was in the US for cancer treatment, and protesting against American influence in Iranian affairs. The incident, known as the Iranian Hostage Crisis, lasted for 444 days, and the hostages were not released until January 20, 1981, the day of President Ronald Reagan's inauguration. This event, along with the failed rescue mission Operation Eagle Claw, significantly contributed to the perception of Carter's administration as ineffective in dealing with international crises, and ultimately affected Carter's re-election campaign.
The crisis was precipitated by a complex history of US-Iranian relations, including the 1953 CIA-assisted coup d'etat that installed the shah and the 1979 Iranian Revolution which led to the establishment of the Islamic Republic under Ayatollah Khomeini. Despite Carter's efforts, including sanctions and a military rescue operation, the hostages remained in captivity until the end of his presidency, casting a shadow over his administration's foreign policy record.