High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ A construction company is analyzing which of its older projects need renovation. Building B was built two years before Building C. Building D was built two years before Building B. The product of Building B's age and Building D's age is at least 195.

If [tex]x[/tex] represents the age of Building C, which inequality represents this situation?

A. [tex]x^2 + 4x + 4 \geq 195[/tex]
B. [tex]x^2 + 4 \geq 195[/tex]
C. [tex]x^2 + 6x + 8 \geq 195[/tex]
D. [tex]x^2 + 8x + 16 \geq 195[/tex]

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]