Elena's mistake lies in her interpretation of the solution x ≥ 55.25 for the inequality 8x + 58 ≥ 500. The solution x ≥ 55.25 suggests that Elena can download 55.25 or more movies to her hard drive, which doesn't make sense because she cannot download a fraction of a movie. In real-world scenarios like this, the number of movies downloaded should be a whole number.
The correct interpretation of the inequality is that Elena can download a maximum of 55 movies, not 55.25 movies. This is because once she downloads the 55th movie, the total data used (58 GB of other files + 55 movies * 8 GB per movie = 498 GB) would nearly reach the capacity of her hard drive (500 GB). However, any additional movie downloaded (even a partial movie) would exceed the hard drive's capacity, which is not feasible.
Therefore, Elena's mistake lies in interpreting the solution as 55.25 movies instead of understanding that the number of movies downloaded should be a whole number, making the correct interpretation x ≥ 55.
