Final answer:
Mexico encouraged Americans to settle in Texas during the Colonial Era.
Step-by-step explanation:
The era during which Mexico encouraged Americans to settle in Texas was the Colonial Era. After gaining independence from Spain in 1821, Mexico passed colonization laws to promote immigration and settlement in the state of Coahuila y Texas. Thousands of Americans, mainly from slave states, moved to Texas and quickly outnumbered the Mexican residents. Mexico's aim to encourage settlement in Texas and the favorable conditions offered attracted many American settlers.