what compromise solved the debate between free & slave states?

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Nature

The debate between free and slave states was initially solved by the Missouri Compromise of 1820. This compromise admitted Missouri as a slave state and Maine as a free state simultaneously, maintaining the balance between slave and free states in the U.S. Senate. Additionally, it prohibited slavery in the remaining Louisiana Territory north of the 36°30' latitude line, except within Missouri's borders. This compromise temporarily settled the sectional conflict over slavery's expansion and kept the Union together for several decades

. Later tensions were addressed by the Compromise of 1850 , which admitted California as a free state, allowed the new territories of Utah and New Mexico to decide on slavery by popular sovereignty, strengthened the Fugitive Slave Act, and abolished the slave trade in Washington, D.C. This compromise was a temporary truce that further delayed the sectional crisis leading to the Civil War

. In summary, the Missouri Compromise was the key initial legislative solution to the debate between free and slave states.