Answer :
Let's solve the problem step-by-step.
We need to find the appropriate inequality to represent the ages of the buildings:
1. Define the variables:
- Let [tex]\( x \)[/tex] be the age of building C.
2. Determine the ages of the other buildings:
- Building B was built 2 years before building C, so the age of building B is [tex]\( x - 2 \)[/tex].
- Building D was built 2 years before building B, so the age of building D is [tex]\( x - 4 \)[/tex].
3. Formulate the inequality:
- We're given that the product of building B's age and building D's age should be at least 195. Therefore, we write:
[tex]\[
(x - 2)(x - 4) \geq 195
\][/tex]
4. Simplify the expression:
- Expand the expression:
[tex]\[
(x - 2)(x - 4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8
\][/tex]
5. Set up the inequality:
- The inequality becomes:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
6. Match with the given options:
- The inequality [tex]\( x^2 - 6x + 8 \geq 195 \)[/tex] corresponds to option B.
Therefore, the correct answer is:
B. [tex]\( x^2 - 6x + 8 \geq 195 \)[/tex]
We need to find the appropriate inequality to represent the ages of the buildings:
1. Define the variables:
- Let [tex]\( x \)[/tex] be the age of building C.
2. Determine the ages of the other buildings:
- Building B was built 2 years before building C, so the age of building B is [tex]\( x - 2 \)[/tex].
- Building D was built 2 years before building B, so the age of building D is [tex]\( x - 4 \)[/tex].
3. Formulate the inequality:
- We're given that the product of building B's age and building D's age should be at least 195. Therefore, we write:
[tex]\[
(x - 2)(x - 4) \geq 195
\][/tex]
4. Simplify the expression:
- Expand the expression:
[tex]\[
(x - 2)(x - 4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8
\][/tex]
5. Set up the inequality:
- The inequality becomes:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
6. Match with the given options:
- The inequality [tex]\( x^2 - 6x + 8 \geq 195 \)[/tex] corresponds to option B.
Therefore, the correct answer is:
B. [tex]\( x^2 - 6x + 8 \geq 195 \)[/tex]
