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The statement that best explains how the Compromise of 1850 attempted to resolve debates over the expansion of slavery is "The compromise allowed California to join the United States as a free state but would allow slavery in southwestern territories."
Under the compromise of 1850, the territories that we're able to choose by popular sovereignty whether or not to allow slavery were New Mexico and Utah.
The United States had defeated the Mexican Army in the Mexican-American War that started in 1846 and ended in 1848. With the victory, the United States got new big portions of land that belonged to México. But many disputes started in the US about the issue of slavery in the territories. That is why under the Compromise of 1850, the government allowed New Mexico and Utah to decide whether or not to allow slavery, while California entered the Union as a free state.