Paul asks what advantage the Jew has. He answers that it is great: the Jews were entrusted with the oracles of God. Their unbelief does not nullify God's faithfulness, and God remains true though every person be a liar. Paul rejects the objection that if our sin highlights God's righteousness, then God should not judge.
He then states that Jews and Greeks are all under sin. He backs this up with a series of quotations from the Psalms and Isaiah: no one is righteous, no one seeks God, all have turned aside, their throats, tongues and feet serve evil and there is no fear of God before their eyes. The law stops every mouth and holds the whole world accountable, because by works of the law no one will be justified; the law brings knowledge of sin.
Verses 21 to 26 bring the turning point: now, apart from the law, the righteousness of God has been revealed, to which the Law and the Prophets bear witness. It comes through faith in Jesus Christ for all who believe, without distinction, since all have sinned and fall short of the glory of God. They are justified freely by his grace through the redemption that is in Christ Jesus. God put him forward as a propitiation by his blood, to be received by faith, to show his righteousness, because he had patiently passed over former sins, so that he might be just and the justifier of the one who has faith in Jesus.
Finally, Paul says all boasting is excluded, because justification is by faith and not by works. God is the God of Jews and Gentiles, and faith does not abolish the law but upholds it.