Answer :
To solve the problem, we need to determine the inequality that represents the ages of the buildings. Let's break it down step by step:
1. Define the Variables:
- Let [tex]\( x \)[/tex] represent the age of Building C.
2. Determine the Ages of the Other Buildings:
- Building B was built two years before Building C, so the age of Building B is [tex]\( x + 2 \)[/tex].
- Building D was built two years before Building B, so the age of Building D is [tex]\( x + 4 \)[/tex].
3. Set Up the Inequality:
- We know that the product of Building B's age and Building D's age should be at least 195. So, we need to express this as an inequality:
[tex]\[
(x + 2) \times (x + 4) \geq 195
\][/tex]
4. Expand the Product:
- Expand the expression [tex]\((x + 2)(x + 4)\)[/tex]:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8
\][/tex]
5. Write the Final Inequality:
- Substitute the expanded expression back into the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct answer is:
B. [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex]
1. Define the Variables:
- Let [tex]\( x \)[/tex] represent the age of Building C.
2. Determine the Ages of the Other Buildings:
- Building B was built two years before Building C, so the age of Building B is [tex]\( x + 2 \)[/tex].
- Building D was built two years before Building B, so the age of Building D is [tex]\( x + 4 \)[/tex].
3. Set Up the Inequality:
- We know that the product of Building B's age and Building D's age should be at least 195. So, we need to express this as an inequality:
[tex]\[
(x + 2) \times (x + 4) \geq 195
\][/tex]
4. Expand the Product:
- Expand the expression [tex]\((x + 2)(x + 4)\)[/tex]:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8
\][/tex]
5. Write the Final Inequality:
- Substitute the expanded expression back into the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct answer is:
B. [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex]
