Answer :
To solve the problem, we need to establish the relationship between the ages of the buildings. Let's define the variable [tex]\( x \)[/tex] as the age of building C.
1. Determine the ages of buildings B and D:
- Building B was built 2 years before building C, so its age is [tex]\( x + 2 \)[/tex].
- Building D was built 2 years before building B, so its age is [tex]\( (x + 2) + 2 = x + 4 \)[/tex].
2. Set up the inequality based on the problem statement:
The problem states that the product of the ages of buildings B and D is at least 195. This can be expressed as:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
3. Expand the expression:
To simplify and solve the inequality, we multiply the expressions:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
[tex]\[
= x^2 + 6x + 8
\][/tex]
4. Formulate the inequality:
We now have the expression:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Based on this reasoning, the correct inequality to represent the situation is [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex], which corresponds to option D in the problem.
1. Determine the ages of buildings B and D:
- Building B was built 2 years before building C, so its age is [tex]\( x + 2 \)[/tex].
- Building D was built 2 years before building B, so its age is [tex]\( (x + 2) + 2 = x + 4 \)[/tex].
2. Set up the inequality based on the problem statement:
The problem states that the product of the ages of buildings B and D is at least 195. This can be expressed as:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
3. Expand the expression:
To simplify and solve the inequality, we multiply the expressions:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
[tex]\[
= x^2 + 6x + 8
\][/tex]
4. Formulate the inequality:
We now have the expression:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Based on this reasoning, the correct inequality to represent the situation is [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex], which corresponds to option D in the problem.
