We've scraped the concrete with a 4 inch blade. The tile is slowly coming up but the black glue won't budge. Someone suggested modified thinset. How is it modified? Will self leveling concrete work over this black stuff (I think it's adhesive.The house was built in 1968.)
What's the most cost effective solution?
Thanks !

This site may be helpful to you. Choosing A Ceramic Tile Thinset Mortar - How To Modified thiset is modified by the manufacturer, you don't do it. You said you used a 4" blade but was it a razor blade or a scraper blade. Scaper won't touch 40 year old adhesive but a razor will. You can put down modified thinset on the black stuff as long as it is fairly level.

If at all possible you should get the old adhesive removed: Adhesive Remover I have used products like this with success: Projects: Adhesive Remover

You will want to work small areas. Don't try to do it all at once. Once you have applied the remover and even after you have removed it, the floor will be very slick for a while. Be cautious and make sure you follow all precautions listed on the container. These chemicals can be dangerous.