I certainly agree here, but this is hardly an argument that Paul denies what he actually affirms in Romans 1, namely that people are ultimately justified by good deeds.4. All are equally have come short of the essential moral law of God found in both inward and outward laws - Rom. 3:9-21
Again, one needs to consider context. Yes, Romans 9-21 describes the sad state of both Jew and Gentile, lost in sin.
But is that the whole picture. Of course not! Why people think they can use this text to refute ultimate justification by good works (I am not necessarily claiming that you, Dr. Walter, are doing so) is a profound mystery since it is so clear that Paul is, in this chunk of chapter 3. describing the state of man apart from the effect of the cross.
Romans 7 and 8 make it clear that, when a person accepts Jesus, they are delivered from the sad Romans 3:9-20 state:
What a wretched man I am! Who will rescue me from this body of death? 25Thanks be to God—through Jesus Christ our Lord!
So Romans 3:9-20 is certainly not an argument against ultimate justification by good deeds, since it is manifestly clear that hte Christian is delivered from such a state.
But it is most certainly a refutation that the non-believer can be justified by their good works.
For reasons I have already provided several times, I entirely agree with this statement. But in embracing this statement, I do not need to deny ultimate justification by good works. And the reasons for this have already been provided.5. Both are equally justified before God according to the SAME LAW - THE LAW OF FAITH - Rom. 3:27-28 which has for its object the person and work of Jesus Christ as the SOLE and SUFFICIENT propitiation/satisfaction of divine justice IN THE PLACE OF all who believe "in" this provision of Christ - Rom. 3:24-26.