7. Where did the United States say the border
between Texas and
Mexico was? What did
Mexico say?

The US said the border between Texas & Mexico was the Rio Grande. Mexico said that border was the Rio Nueces.

Explanation:

The boundary between Texas and Mexico was disputed, with the Republic of Texas and the USA asserting it to be the Rio Grande River (which it what the border is in the present day) and Mexico claiming it to be the more-northern Nueces River. Both Mexico and the USA claimed the disputed area and sent troops. Polk sent U.S. Army troops to the area; he also sent a diplomatic mission to Mexico to try to negotiate the sale of territory. U.S. troops' presence was designed to lure Mexico into starting the conflict (which was successful, putting the onus (responsibility) on Mexico and allowing Polk to argue to Congress that a declaration of war should be issued. Mexican forces attacked U.S. forces, and the United States Congress declared war on Mexico in May 11, 1846 -- that wasn't the start of the fighting however; that began 16 days earlier on April 25.