One week after unveiling her debut single, "Invisible," Skylar Grey tells Billboard.com that the vulnerable track is a perfect introduction to first solo album "Invinsible" (pronounced 'invincible'), which will be released this fall.

"It's the very beginning of the story that I'm telling on this album, so chronologically, it makes sense to release that part of my story first" says Grey, who began her career as a struggling singer/songwriter in Los Angeles. "I was depressed and broke and had nobody around and was feeling invisible to the world. That's what that song's about, that very first step… and so, within the album, you go on that journey of how I became invincible, and i think it's gonna be a story that a lot of people can relate to."

Skylar Grey Drops 'Dance Without You' Track As Free Download: Listen

After earning a Song of the Year Grammy nomination for co-penning Eminem's Hot 100 chart-topper "Love the Way You Lie," Grey translated her songwriting talents to guest vocal spots on Dr. Dre's "I Need a Doctor," Lupe Fiasco's "Words I Never Said" and Diddy-Dirty Money's "Coming Home." Grey, who wrote the tracks on "Invinsible" throughout the past year, says that she's "98 percent finished" work on the debut album, which was helmed entirely by white-hot pop producer Alex da Kid ("I Need a Doctor," B.o.B's "Airplanes").

"One of the things I love about Alex is that he tells me when things suck," Grey says with a laugh. "I really almost want to punch him in the face sometimes. Making a comment like, 'Oh, I think you can do better,' it might hurt at first, [but] then I'll go back and tweak the song, and it'll end up being better. So I'll agree with him at the end of the day, so it's only for the best that we have our differences."

Grey says that "Invinsible" does not have a firm release date yet, and won't have one until "Invisible" is given time to gain momentum at pop radio (a teaser track, "Dance Without You," was also released earlier this month). While she finalizes her debut full-length and prepares her live show -- an appearance at Lollapalooza in August will be followed by an in-the-works fall tour that may hit Europe and the U.S. -- Grey says that her songwriting output for other artists will have to slow down.

"Writing for other people isn't part of my plan at this time," she says, "but it will probably happen again in the future."

Skylar Grey Parlays Hit-Making for Eminem, Dre Into Solo Career