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Answer :
Let's solve this problem step-by-step to find the correct inequality.
1. Identify the ages of the buildings in terms of [tex]\(x\)[/tex]:
- Building C's age is [tex]\(x\)[/tex].
- Building B is two years older than Building C, so its age is [tex]\(x - 2\)[/tex].
- Building D is two years older than Building B, so its age is [tex]\((x - 2) - 2 = x - 4\)[/tex].
2. Set up the product equality:
- The problem states that the product of the ages of Building B and Building D must be at least 195. Therefore, the inequality we are dealing with is: [tex]\((x - 2)(x - 4) \geq 195\)[/tex].
3. Expand the expression:
- Multiply the expressions:
[tex]\[
(x - 2)(x - 4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8
\][/tex]
4. Form the inequality:
- Now, we form the inequality:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
This matches the description of option D:
[tex]\(x^2 - 6x + 8 \geq 195\)[/tex].
So, the correct answer is option D.
1. Identify the ages of the buildings in terms of [tex]\(x\)[/tex]:
- Building C's age is [tex]\(x\)[/tex].
- Building B is two years older than Building C, so its age is [tex]\(x - 2\)[/tex].
- Building D is two years older than Building B, so its age is [tex]\((x - 2) - 2 = x - 4\)[/tex].
2. Set up the product equality:
- The problem states that the product of the ages of Building B and Building D must be at least 195. Therefore, the inequality we are dealing with is: [tex]\((x - 2)(x - 4) \geq 195\)[/tex].
3. Expand the expression:
- Multiply the expressions:
[tex]\[
(x - 2)(x - 4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8
\][/tex]
4. Form the inequality:
- Now, we form the inequality:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
This matches the description of option D:
[tex]\(x^2 - 6x + 8 \geq 195\)[/tex].
So, the correct answer is option D.
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