Select the correct answer.

A construction company is analyzing which of its older projects need renovation. Building B was built two years before Building C. Building D was built two years before Building B. The product of Building B's age and Building D's age is at least 195. If [tex]x[/tex] represents the age of Building C, which inequality represents this situation?

A. [tex]x^2 + 4 \geq 195[/tex]

B. [tex]x^2 + 6x + 8 \geq 195[/tex]

C. [tex]x^2 + 8x + 16 \geq 195[/tex]

D. [tex]x^2 + 4x + 4 \geq 195[/tex]

To solve the problem, we need to understand the ages of the buildings in relation to each other:

1. Define [tex]$ x $[/tex] as the age of Building C.

2. Building B was built two years before Building C. Therefore, the age of Building B is [tex]$ x + 2 $[/tex].

3. Building D was built two years before Building B. Therefore, the age of Building D is [tex]$ x + 4 $[/tex].

The problem states that the product of the ages of Building B and Building D must be at least 195. This means:

[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]

Now, let's expand the left side of the inequality:

- Multiply [tex]$ x + 2 $[/tex] and [tex]$ x + 4 $[/tex]:

[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]

Combine like terms:

[tex]\[
x^2 + 6x + 8
\][/tex]

So, the inequality representing the situation is:

[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]

Therefore, the correct answer is B. [tex]$ x^2 + 6x + 8 \geq 195 $[/tex].