Final answer:
The correct algebraic expression represented by the model with five tiles labeled x and seven tiles labeled minus 1 is (2x - 3) - (-3x + 4), which simplifies to 5x - 7 and matches the model.
Step-by-step explanation:
The student is presented with a model consisting of algebra tiles, with five tiles labeled x and seven tiles labeled minus 1. Given this information, we need to identify which algebraic expression the tiles represent. When we look at the options provided, we are looking for an expression that represents 5 x-tiles and 7 negative unit tiles.
Let's work through the options and compare:
1) (-2x + 3) does not match as it has only 2 x-tiles.
2) (3x - 4) also does not match as it has 3 x-tiles.
3) (-2x + 3) - (3x - 4) is more complex, and after applying subtraction, it does not match.
4) (2x - 3) again, does not match because of the number of x-tiles.
5) (-3x + 4) again fails to match.
6) (2x - 3) - (-3x + 4) simplifies to 5x - 7, which matches our model of five x-tiles and seven negative units.
Therefore, the correct answer is (2x - 3) - (-3x + 4).