Here "believes" means "trusts." AT: "in order that he may make everyone who trusts in him right before God" (See: [[rc://en/ta/man/translate/figs-explicit]])
Paul speaks of "righteousness" as if it were alive and able to move. AT: "how the law makes a person right before God" (See: [[rc://en/ta/man/translate/figs-personification]])
In order to be made right with God through the law, a person would have to keep the law perfectly, which is not possible. AT: "The person who perfectly obeys the law will live because the law will make him right before God" (See: [[rc://en/ta/man/translate/figs-explicit]])