Final answer:
Justices interpreting unclear laws must follow the Constitution, adhere to statutory law and precedents, and thoroughly prepare for and consider the oral arguments presented before them.
Step-by-step explanation:
When justices face the challenge of interpreting laws that have unclear language, they must engage in a complex process of decision-making that takes into account various sources of law and precedent. First, they must consider the Constitution and its relevant provisions, as it is the supreme law of the land.
In instances where the Constitution conflicts with legislative acts, the latter may be deemed invalid, as established in the landmark case Marbury v. Madison. Secondly, judges are expected to follow statutory law, adhering to existing federal statutes, while also acknowledging their position within the governmental structure and striving not to provoke conflict with legislative bodies.
Lastly, when preparing for oral arguments, justices and their clerks analyze briefs and legal arguments to grasp the nuances of each case before reaching a decision, which requires weighing in personal interpretations and legal reasoning to arrive at a conclusion that upholds the integrity of the law.