Rom 1:17
For in the gospel a righteousness from God is revealed, a righteousness that is by faith from first to last, just as it is written: "The righteous will live by faith."
The only way for a human being, a sinner, to reach God is to be justified by God's grace. In fact, that is the gospel. Thus, the Bible says that the gospel is to be justified by one's faith. The apostle Paul says, "For in the gospel a righteousness from God is revealed, a righteousness that is by faith from first to last"(Rom 1:17).
The gospel does not only reveal God's redemptive work of salvation for us, but also reveals the divinity of God. Namely, God's righteousness is revealed in the gospel. God is always righteous, is the source of righteousness, and act out His righteousness. A human, an unrighteous one, can reach God and become righteous only through Jesus Christ.
In the Old Testament, God blessed those who fear Him, and keeps purity. "He who has clean hands and a pure heart, who does not lift up his soul to an idol or swear by what is false. He will receive blessing from the LORD and vindication from God his Savior"(Ps 24:4, 5). "With me are riches and honor, enduring wealth and prosperity"(Prov 8:18).
On the other hand, in the New Testament, justification does not mean 'justifying' someone, but it means to consider a sinner as 'righteous one.' Being righteous before God does not mean a sinner becomes a good and righteous one, but to consider one righteousness, without sin. This is justification in a theological sense. And we receive justification by faith. Paul quoted the prophet Habakkuk and wrote, "The righteous will live by his faith"(Hab 2:4).
We should all be justified to live righteously. Thus, we have to be justified by faith, and live by faith. This is the meaning of "a righteousness that is by faith from first to last"(Rom 1:17). Quite often, authors of the Bible use the same word with different meanings(2 Cor 2:16; Ps 84:7). 'Faith' in Rom 1:17 implies a righteousness only by faith, and also implies a depended faith, and sharing faith with others.
If we are justified by God, we should live by faith to please God. "Each of you should look not only to your own interests, but also to the interests of others"(Phil 2:4).