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Answer :
To solve this problem, let's analyze the information provided about the buildings and their ages:
1. Let [tex]\( x \)[/tex] represent the age of Building C.
2. Building B was built two years before Building C, so Building B's age is [tex]\( x + 2 \)[/tex].
3. Building D was built two years before Building B, making Building D's age [tex]\( x + 4 \)[/tex].
We know from the problem that the product of Building B's age and Building D's age is at least 195. Mathematically, this is expressed as:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
Now, let's expand this inequality:
1. Multiply the terms:
[tex]\[
(x + 2)(x + 4) = x \cdot x + x \cdot 4 + 2 \cdot x + 2 \cdot 4
\][/tex]
2. Simplify the resulting expression:
[tex]\[
= x^2 + 4x + 2x + 8
\][/tex]
3. Combine like terms:
[tex]\[
= x^2 + 6x + 8
\][/tex]
The inequality then becomes:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct answer is:
B. [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex]
1. Let [tex]\( x \)[/tex] represent the age of Building C.
2. Building B was built two years before Building C, so Building B's age is [tex]\( x + 2 \)[/tex].
3. Building D was built two years before Building B, making Building D's age [tex]\( x + 4 \)[/tex].
We know from the problem that the product of Building B's age and Building D's age is at least 195. Mathematically, this is expressed as:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
Now, let's expand this inequality:
1. Multiply the terms:
[tex]\[
(x + 2)(x + 4) = x \cdot x + x \cdot 4 + 2 \cdot x + 2 \cdot 4
\][/tex]
2. Simplify the resulting expression:
[tex]\[
= x^2 + 4x + 2x + 8
\][/tex]
3. Combine like terms:
[tex]\[
= x^2 + 6x + 8
\][/tex]
The inequality then becomes:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct answer is:
B. [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex]
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