Answer :
To solve the problem, let's go through it step-by-step:
1. Understand the Variables:
- Let [tex]\( x \)[/tex] represent the age of building C.
2. Determine the Ages of Buildings B and D:
- Building B was built two years before building C, so its age is [tex]\( x + 2 \)[/tex].
- Building D was built two years before building B, so its age is [tex]\( x + 4 \)[/tex].
3. Set Up the Inequality:
- We know the product of the ages of buildings B and D must be at least 195, which leads to the inequality:
[tex]\[
(x + 2) \times (x + 4) \geq 195
\][/tex]
4. Expand the Expression:
- Expanding [tex]\((x + 2) \times (x + 4)\)[/tex], we have:
[tex]\[
x^2 + 4x + 2x + 8 = x^2 + 6x + 8
\][/tex]
5. Form the Inequality:
- Substitute the expanded expression back into the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
6. Identify the Correct Answer:
- The inequality [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex] matches option C in the given choices.
Therefore, the correct option that represents the situation is:
C. [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex]
1. Understand the Variables:
- Let [tex]\( x \)[/tex] represent the age of building C.
2. Determine the Ages of Buildings B and D:
- Building B was built two years before building C, so its age is [tex]\( x + 2 \)[/tex].
- Building D was built two years before building B, so its age is [tex]\( x + 4 \)[/tex].
3. Set Up the Inequality:
- We know the product of the ages of buildings B and D must be at least 195, which leads to the inequality:
[tex]\[
(x + 2) \times (x + 4) \geq 195
\][/tex]
4. Expand the Expression:
- Expanding [tex]\((x + 2) \times (x + 4)\)[/tex], we have:
[tex]\[
x^2 + 4x + 2x + 8 = x^2 + 6x + 8
\][/tex]
5. Form the Inequality:
- Substitute the expanded expression back into the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
6. Identify the Correct Answer:
- The inequality [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex] matches option C in the given choices.
Therefore, the correct option that represents the situation is:
C. [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex]