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. Therefore, the number of playlists on Liam's app is 4X.
The total number of playlists on both their apps is at least 45, so X + 4X ≥ 45.
This simplifies to 5X ≥ 45.
Dividing both sides of the inequality by 5, we get X ≥ 9.
Therefore, the solution set for X, representing the number of playlists on Ashley's app, is x≥9.