Final answer:
The correct inequality to represent the situation is (x - 2)(x + 2) ≥ 195, which simplifies to x^2 ≥ 199. However, none of the provided options in the question match this inequality, so there might be a typo in the student's options or an error in the question itself.
Step-by-step explanation:
The student is asking how to represent a mathematical situation involving the ages of buildings with an inequality. If we let x be the age of Building C, then Building B was built two years before, so it is x - 2 years old. Building D was built two years after Building C, so it is x + 2 years old. The question states that the product of Building B's age and Building D's age is at least 195, which translates to the inequality (x - 2)(x + 2) ≥ 195.
Expanding this out, we get x2 - 4 ≥ 195. When we move -4 to the other side of the inequality, we have x2 ≥ 199, which is not one of the provided options. Hence, the correct inequality must be the one that's algebraically equivalent once simplified properly. Option B, x2 + 4 > 195, when simplified, gives us x2 > 191, which is not equivalent to our inequality. However, none of the provided options match exactly, which indicates there may be a typo or mistake in the options provided by the student or the question itself.