Answer :
To solve this problem, we need to represent the age relationships between the buildings with an inequality. Let's break it down step by step.
1. Variables and Relationships:
- Let [tex]\( x \)[/tex] be the age of building C.
- Building B was built 2 years before building C. Therefore, the age of building B is [tex]\( x + 2 \)[/tex].
- Building D was built 2 years before building B. Thus, the age of building D is [tex]\( (x + 2) + 2 = x + 4 \)[/tex].
2. Product of Ages:
- The product of the ages of building B and building D must be at least 195. This gives us the inequality:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
3. Expand and Simplify:
- To simplify the inequality, we first expand the product on the left-hand side:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
Combine like terms:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
4. Form the Inequality:
- The final inequality that represents the situation is:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct inequality is
[tex]\[
\boxed{x^2 + 6x + 8 \geq 195}
\][/tex]
This corresponds to option A.
1. Variables and Relationships:
- Let [tex]\( x \)[/tex] be the age of building C.
- Building B was built 2 years before building C. Therefore, the age of building B is [tex]\( x + 2 \)[/tex].
- Building D was built 2 years before building B. Thus, the age of building D is [tex]\( (x + 2) + 2 = x + 4 \)[/tex].
2. Product of Ages:
- The product of the ages of building B and building D must be at least 195. This gives us the inequality:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
3. Expand and Simplify:
- To simplify the inequality, we first expand the product on the left-hand side:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
Combine like terms:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
4. Form the Inequality:
- The final inequality that represents the situation is:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct inequality is
[tex]\[
\boxed{x^2 + 6x + 8 \geq 195}
\][/tex]
This corresponds to option A.
