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Answer :
Let's solve the problem step-by-step to identify the correct inequality:
1. Identify the Variables:
- Let [tex]\( x \)[/tex] be the age of building C.
2. Determine Ages of Other Buildings:
- Building B is two years older than building C. So, the age of Building B is [tex]\( x + 2 \)[/tex].
- Building D is two years older than Building B. So, the age of Building D is [tex]\( x + 4 \)[/tex].
3. Set Up the Inequality:
- The problem states that the product of Building B's age and Building D's age is at least 195. This translates to the following inequality:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
4. Expand the Equation:
- First, expand the left-hand side of the inequality:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
- Combine like terms:
[tex]\[
x^2 + 6x + 8
\][/tex]
5. Complete the Inequality:
- Place the expanded expression in the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
6. Select the Correct Answer:
- From the expanded inequality, we conclude that the correct inequality is:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
- The correct answer is option D: [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex].
1. Identify the Variables:
- Let [tex]\( x \)[/tex] be the age of building C.
2. Determine Ages of Other Buildings:
- Building B is two years older than building C. So, the age of Building B is [tex]\( x + 2 \)[/tex].
- Building D is two years older than Building B. So, the age of Building D is [tex]\( x + 4 \)[/tex].
3. Set Up the Inequality:
- The problem states that the product of Building B's age and Building D's age is at least 195. This translates to the following inequality:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]
4. Expand the Equation:
- First, expand the left-hand side of the inequality:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
- Combine like terms:
[tex]\[
x^2 + 6x + 8
\][/tex]
5. Complete the Inequality:
- Place the expanded expression in the inequality:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
6. Select the Correct Answer:
- From the expanded inequality, we conclude that the correct inequality is:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]
- The correct answer is option D: [tex]\( x^2 + 6x + 8 \geq 195 \)[/tex].
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