Although not used much in normal conversation, righteous and righteousness are important biblical words. An important point – but one is difficult to see from English translations – is that these two words are very closely related to “just” and “justify”. In Greek all four words come from the same word root (dikaio). “Justify” literally means to “declare righteous”. It is a term taken from the courtroom where it was used to describe a judge’s verdict of declaring someone righteous or not guilty. From the perspective of the Greek of the New Testament there is no difference between the two questions: “How can I be righteous”” or “How can I be justified?”
Therefore a most important passage in this regard is Romans 3:20: “Therefore by the deeds of the law there shall no flesh be justified (declared righteous) in his sight, for by the law is the knowledge of sin.” A most important question is what does the word “law” refer to in this passage? It is obvious how the LDS Church interprets it. A footnote in the LDS edition of the Bible references this to the Law of Moses.
But that doesn’t fit the context. From 1:18 through 3:20 Paul argues extensively that all people, both Jew and Gentile, are under God’s wrath because of sin. Starting with 3:9 he begins his summation: “for we have before proved both Jews and Gentiles, that they are all under sin.” The “no flesh” of 3:20 does not just refer to Jews who had the Law of Moses. It refers to all people and, by extension, all law. No matter what law a person holds to and tries to follow – it will not be a way for that person to be declared righteous (justified).
“But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference: For all have sinned, and come short of the glory of God; Being justified freely by his grace through the redemption that is in Christ Jesus.”
How to be righteous before God? Not by deeds but by belief. The contrast Paul sets up here is not between righteousness through deeds alone and faith and deeds. No, the contrast Paul makes is between righteousness either through deeds or faith. “Therefore we conclude that a man is justified by faith without the deeds of the law.” (v. 28) Interestingly, the LDS Bible’s footnotes the word “without” with GR which indicates an alternate translation of the Greek. The alternate translation: “apart from, without intervention”. ‘Therefore we conclude that a man is justified by faith apart from, without the intervention of the deeds of the law.” In the very next verse Paul again mentions both Jews and Gentiles. From the context it is obvious that his point is that people are justified through faith apart from any deeds of any law.