How to add songs, from CDs, to my iPhone without deleting all my old music?

I just bought a new computer and all of my previous music files are from CDs, as well as the new files I want to add. However, when I try to sync my iPhone is asks if I want to remove all of my old music to sync with my library. How can I add new songs without losing old files.

Just put the new CD's on the computer, DO NOT sync your phone and just drag the songs onto your phone as if you were making a new playlist. I do this all the time to transfer songs from my dad's computer to my computer. Hope this helped.

When you connect your phone to iTunes, tick the box in the menu "manage music