Answer :
To solve the problem, we need to establish the ages of the buildings based on the information provided:
1. Let's represent the age of building C as [tex]\( x \)[/tex].
2. According to the problem, 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. So, the age of Building D is [tex]\( (x + 2) + 2 = x + 4 \)[/tex].
4. We are given that the product of the ages of Building B and Building D is at least 195. Mathematically, this can be written as:
[tex]\[
(x + 2) \times (x + 4) \geq 195
\][/tex]
5. To solve this, we'll expand the left side of the inequality:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
6. Combining like terms, we get:
[tex]\[
x^2 + 6x + 8
\][/tex]
7. Plugging this back into the inequality gives us:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
This inequality accurately represents the situation described. Therefore, the correct answer is:
D. [tex]\(x^2 + 6x + 8 \geq 195\)[/tex]
1. Let's represent the age of building C as [tex]\( x \)[/tex].
2. According to the problem, 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. So, the age of Building D is [tex]\( (x + 2) + 2 = x + 4 \)[/tex].
4. We are given that the product of the ages of Building B and Building D is at least 195. Mathematically, this can be written as:
[tex]\[
(x + 2) \times (x + 4) \geq 195
\][/tex]
5. To solve this, we'll expand the left side of the inequality:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
6. Combining like terms, we get:
[tex]\[
x^2 + 6x + 8
\][/tex]
7. Plugging this back into the inequality gives us:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
This inequality accurately represents the situation described. Therefore, the correct answer is:
D. [tex]\(x^2 + 6x + 8 \geq 195\)[/tex]
