Let's represent the number of playlists on Ashley's app as X.
According to the given information, the number of playlists on Liam's app is 4 times the number of playlists on Ashley's app. So, the number of playlists on Liam's app would be 4*X.
The total number of playlists on both their apps is at least 45. So, X + 4*X ≥ 45.
Combining like terms, we get 5*X ≥ 45.
Dividing both sides by 5, we have X ≥ 9.
Therefore, the solution set for X, representing the number of playlists on Ashley's app, is X ≥ 9.