Let's break down the problem step by step:
1. Define the Variables:
- Let [tex]\( x \)[/tex] represent the age of Building C.
- Since Building B was built two years before Building C, the age of Building B is [tex]\( x + 2 \)[/tex].
- Likewise, since Building D was built two years before Building B, the age of Building D is [tex]\( x + 4 \)[/tex].
2. Age Product Condition:
- The product of Building B's age and Building D's age is at least 195.
- Mathematically, this is represented as [tex]\((x + 2)(x + 4) \geq 195\)[/tex].
3. Expand the Product:
- Expanding [tex]\((x + 2)(x + 4)\)[/tex]:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8
\][/tex]
4. Form the Inequality:
- According to the given condition, this expanded expression must be at least 195:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct inequality that represents the situation given in the problem is:
[tex]\[ \boxed{x^2 + 6x + 8 \geq 195} \][/tex]
This corresponds to option B.
