What did the united states do to encourage texas to give up some of its land?

Offered to pay off its debt.

Explanation:

The Mexican War (1846–48) left Texas in a severe battle with the national government over the state's claim to a big part of New Mexico.

Under the Compromise of 1850, Texas abandoned its land demands in exchange for the federal assumption of the state's public debt.

The compromise, brokered by Whig Senator Henry Clay, Democratic Senator Stephen Douglas, and President Millard Fillmore, produced the current boundaries of the State of Texas.

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