the Court’s task is to interpret the meaning of a law, to decide whether a law is relevant to a particular set of facts, or to rule on how a law should be applied. Lower courts are obligated to follow the precedent set by the Supreme Court when rendering decisions.> https://www.whitehouse.gov/about-the-white-house/the-judicial-branch/

From what I understand, by getting the Supreme Court to interpret the law and how it is being violated they are solving problems by setting precedent for the lower courts and other states where cases are similar.