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?

1) [tex]x^2 + 6x + 8 > 195[/tex]
2) [tex]x^2 + 4x + 4 > 195[/tex]
3) [tex]x^2 + 8x + 16 > 195[/tex]
4) [tex]x^2 + 4 > 195[/tex]

The inequality that represents the situation is x² + 8x + 16 > 195. Building C is the newest building and has an age represented by x, while building B was built two years before building C, and building D was built two years before building B.

Explanation:

The inequality that represents the situation is x² + 8x + 16 > 195. By analyzing the information given, we can determine that building C is the newest building and has an age represented by x. Building B was built two years before building C, so its age can be represented as (x-2). Building D was built two years before building B, so its age can be represented as (x-4). The product of building B's age and building D's age is at least 195, which gives us the equation (x-2)(x-4) ≥ 195. Simplifying this equation gives us x² + 8x + 16 > 195.

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