Is it possible for a business to be solvent but not profitable? Why or why not?

Yes i think it is possible, as long as you don't lose money. I mean a business can run very well, maybe doesn't make a huge profit but still it's not like the business id going down. It is possible for a business to make just enough money so the business does not shut down. You know enough money like a breaking point. In fact i'm pretty sure there are a lot of business out there that make just enough money so they don't actually need to close their businesses