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Answer :
To solve the problem, let's break it down step-by-step:
1. Understand the Ages of the Buildings:
- 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, so the age of Building D is [tex]\( x + 4 \)[/tex].
2. Set Up the Inequality:
- We are given that the product of the ages of Buildings B and D is at least 195. This can be written as:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
3. Expand the Product:
- Multiply the expressions:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
- Simplify:
[tex]\[
x^2 + 6x + 8
\][/tex]
4. Formulate the Inequality:
- Now, place the expression into the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct inequality that represents this situation is:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
This matches with option A.
1. Understand the Ages of the Buildings:
- 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, so the age of Building D is [tex]\( x + 4 \)[/tex].
2. Set Up the Inequality:
- We are given that the product of the ages of Buildings B and D is at least 195. This can be written as:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
3. Expand the Product:
- Multiply the expressions:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
- Simplify:
[tex]\[
x^2 + 6x + 8
\][/tex]
4. Formulate the Inequality:
- Now, place the expression into the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct inequality that represents this situation is:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
This matches with option A.
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