Final answer:
The Supreme Court invalidated unequal legislative districts for the U.S. House in the case of Baker v. Carr (1962), establishing the principle of "one-man, one-vote".
Step-by-step explanation:
In the case of Baker v. Carr (1962), the Supreme Court ruled that redistricting created an option for the federal courts to decide redistricting cases. This landmark decision established the principle of "one-man, one-vote," which meant that states could not give rural voters a disproportionate sway in state legislatures. It invalidated unequal legislative districts for the U.S. House, ensuring that each district would have roughly the same number of people, and therefore, one person's vote in a congressional election would be worth as much as another's.