Answer :
Let [tex]$x$[/tex] represent the age of building [tex]$C$[/tex]. According to the problem:
1. Building [tex]$B$[/tex] was built two years before building [tex]$C$[/tex]. Therefore, the age of building [tex]$B$[/tex] is
[tex]$$x + 2.$$[/tex]
2. Building [tex]$D$[/tex] was built two years before building [tex]$B$[/tex]. Hence, the age of building [tex]$D$[/tex] is
[tex]$$ (x+2) + 2 = x + 4.$$[/tex]
The product of the ages of buildings [tex]$B$[/tex] and [tex]$D$[/tex] is given to be at least 195. This means:
[tex]$$
(x + 2)(x + 4) \geq 195.
$$[/tex]
Expanding the left-hand side:
[tex]$$
(x+2)(x+4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8.
$$[/tex]
Thus, the inequality becomes:
[tex]$$
x^2 + 6x + 8 \geq 195.
$$[/tex]
Comparing with the given options, we see that this inequality matches option D:
[tex]$$
x^2 + 6x + 8 \geq 195.
$$[/tex]
Therefore, the correct answer is option D, which corresponds to answer number 4.
1. Building [tex]$B$[/tex] was built two years before building [tex]$C$[/tex]. Therefore, the age of building [tex]$B$[/tex] is
[tex]$$x + 2.$$[/tex]
2. Building [tex]$D$[/tex] was built two years before building [tex]$B$[/tex]. Hence, the age of building [tex]$D$[/tex] is
[tex]$$ (x+2) + 2 = x + 4.$$[/tex]
The product of the ages of buildings [tex]$B$[/tex] and [tex]$D$[/tex] is given to be at least 195. This means:
[tex]$$
(x + 2)(x + 4) \geq 195.
$$[/tex]
Expanding the left-hand side:
[tex]$$
(x+2)(x+4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8.
$$[/tex]
Thus, the inequality becomes:
[tex]$$
x^2 + 6x + 8 \geq 195.
$$[/tex]
Comparing with the given options, we see that this inequality matches option D:
[tex]$$
x^2 + 6x + 8 \geq 195.
$$[/tex]
Therefore, the correct answer is option D, which corresponds to answer number 4.
