Final answer:
The equation 2x-7=15 has one unique solution, x=11, whereas the inequality 2x-7<15 represents an infinite range of solutions (all x values less than 11). Therefore, the correct answer to the question is that the first equation has one solution, and the second equation has infinite solutions.
Step-by-step explanation:
When comparing the solutions of the equations 2x-7=15 and 2x-7<15, we find that while the former is a linear equation with a single solution, the latter is an inequality representing a range of solutions. We solve the equation 2x-7=15 by adding 7 to both sides, yielding 2x=22 and then dividing both sides by 2 to get x=11. This equation has one unique solution making it a linear equation. On the other hand, the inequality 2x-7<15 represents all x values that make the inequality true after we solve for x in a similar manner by adding 7 to both sides and dividing by 2, giving us x<11. This means any x-value less than 11 is a solution, suggesting an infinite number of solutions.
Therefore, the correct answer to the question is that the first equation has one solution, and the second equation has infinite solutions. We can also solidify our understanding that, generally, linear equations have a certain number of distinct solutions (one, in this case), whereas inequalities like the second equation represent a set of values, providing multiple or infinite solutions.