Something is definitely lost when we read Scripture in short bites or proof texts rather than seeing the entire thought patterns that lay out over an entire chapter or a few chapters.
I know many proof texts that are rightly quoted from the pulpit, but are never seen in their greater context meaning. When you read those in the paragraph where they were born, they burst with meaning.
There are several such salvation theology verses in Romans. I challenge you to read chapters 1-3 altogether sometime. You will see popularly quoted verses, but what you will see more is an amazing picture of salvation by faith alone, apart from the deeds of the law or grace:
Chap. 1 - The wickedness of the wicked before God
Chap. 2 - The wickedness of the self-righteous law keepers before God
Chap. 3 - The wickedness of everyman before God; righteousness apart from the law; justification by faith
What an exciting and faith-building read these three chapters are! What joy they bring to the heart of someone clinging to faith in Jesus Christ alone.