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Answer :
To solve the problem, let's follow these steps:
1. Understand the relationship between the buildings and their ages:
- Building C's age is represented by [tex]\( x \)[/tex].
- Building B was built two years before Building C, so the age of Building B is [tex]\( x - 2 \)[/tex].
- Building D was built two years before Building B, therefore the age of Building D is [tex]\( x - 4 \)[/tex].
2. Translate the information into an inequality:
- The problem states that the product of the ages of Building B and Building D is at least 195. This can be expressed as:
[tex]\[
(x - 2) \times (x - 4) \geq 195
\][/tex]
3. Simplify and expand the inequality:
- Distribute the expression:
[tex]\[
(x - 2)(x - 4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8
\][/tex]
4. Set up the inequality:
- Now we have:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
The inequality representing the situation is:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
The correct answer choice is not listed in the given options, but based on our understanding, this is the resulting expression from translating the given problem into a mathematical expression. Thus, you should use the process to understand and verify the relationships to arrive at the correct inequality.
1. Understand the relationship between the buildings and their ages:
- Building C's age is represented by [tex]\( x \)[/tex].
- Building B was built two years before Building C, so the age of Building B is [tex]\( x - 2 \)[/tex].
- Building D was built two years before Building B, therefore the age of Building D is [tex]\( x - 4 \)[/tex].
2. Translate the information into an inequality:
- The problem states that the product of the ages of Building B and Building D is at least 195. This can be expressed as:
[tex]\[
(x - 2) \times (x - 4) \geq 195
\][/tex]
3. Simplify and expand the inequality:
- Distribute the expression:
[tex]\[
(x - 2)(x - 4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8
\][/tex]
4. Set up the inequality:
- Now we have:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
The inequality representing the situation is:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
The correct answer choice is not listed in the given options, but based on our understanding, this is the resulting expression from translating the given problem into a mathematical expression. Thus, you should use the process to understand and verify the relationships to arrive at the correct inequality.
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