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Answer :
To solve the problem, we need to determine the correct inequality that represents the ages of the buildings.
1. Define Variables:
- Let [tex]\( x \)[/tex] be the age of building C.
- Since building B was built two years before building C, the age of building B is [tex]\( x + 2 \)[/tex].
- Building D was built two years before building B, which makes building D's age [tex]\( x + 4 \)[/tex].
2. Set Up the Inequality:
- We are told that the product of the ages of building B and building D is at least 195. This translates to:
[tex]\[
(x + 2) \times (x + 4) \geq 195
\][/tex]
3. Expand and Simplify:
- Expand the product on the left side:
[tex]\[
(x + 2)(x + 4) = x \times x + 4x + 2x + 2 \times 4
\][/tex]
- Combine like terms:
[tex]\[
x^2 + 4x + 2x + 8 = x^2 + 6x + 8
\][/tex]
4. Write the Inequality:
- Combine it all to form the complete inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct inequality that represents this situation is:
A. [tex]\(x^2 + 6x + 8 \geq 195\)[/tex]
1. Define Variables:
- Let [tex]\( x \)[/tex] be the age of building C.
- Since building B was built two years before building C, the age of building B is [tex]\( x + 2 \)[/tex].
- Building D was built two years before building B, which makes building D's age [tex]\( x + 4 \)[/tex].
2. Set Up the Inequality:
- We are told that the product of the ages of building B and building D is at least 195. This translates to:
[tex]\[
(x + 2) \times (x + 4) \geq 195
\][/tex]
3. Expand and Simplify:
- Expand the product on the left side:
[tex]\[
(x + 2)(x + 4) = x \times x + 4x + 2x + 2 \times 4
\][/tex]
- Combine like terms:
[tex]\[
x^2 + 4x + 2x + 8 = x^2 + 6x + 8
\][/tex]
4. Write the Inequality:
- Combine it all to form the complete inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
Therefore, the correct inequality that represents this situation is:
A. [tex]\(x^2 + 6x + 8 \geq 195\)[/tex]
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