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Let X represent the number of playlists on Ashley's app.
The number of playlists on Liam's app would be 4X.
The total number of playlists on both their apps is at least 45, so X + 4X ≥ 45.
Combining like terms, we get 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.