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Answer :
To solve the problem of finding the inequality that represents the product of two consecutive odd integers being less than 76, let's break it down step by step:
1. Identify the Consecutive Odd Integers:
- If [tex]\( n \)[/tex] is our first odd integer, then the next consecutive odd integer would be [tex]\( n + 2 \)[/tex].
- For example, if [tex]\( n = 3 \)[/tex], [tex]\( n + 2 = 5 \)[/tex].
2. Write the Expression for the Product:
- The product of these two consecutive odd integers can be expressed as:
[tex]\[
n \times (n + 2)
\][/tex]
3. Set Up the Inequality:
- According to the problem, the product needs to be less than 76. Therefore, we have the inequality:
[tex]\[
n \times (n + 2) < 76
\][/tex]
4. Choose the Correct Option:
- Based on the options provided, the inequality is [tex]\( n(n + 2) < 76 \)[/tex]. This matches the requirements of the scenario described.
Thus, the correct inequality that represents this scenario is:
[tex]\[
n(n + 2) < 76
\][/tex]
This inequality captures the relationship described, where the product of two consecutive odd integers is less than 76.
1. Identify the Consecutive Odd Integers:
- If [tex]\( n \)[/tex] is our first odd integer, then the next consecutive odd integer would be [tex]\( n + 2 \)[/tex].
- For example, if [tex]\( n = 3 \)[/tex], [tex]\( n + 2 = 5 \)[/tex].
2. Write the Expression for the Product:
- The product of these two consecutive odd integers can be expressed as:
[tex]\[
n \times (n + 2)
\][/tex]
3. Set Up the Inequality:
- According to the problem, the product needs to be less than 76. Therefore, we have the inequality:
[tex]\[
n \times (n + 2) < 76
\][/tex]
4. Choose the Correct Option:
- Based on the options provided, the inequality is [tex]\( n(n + 2) < 76 \)[/tex]. This matches the requirements of the scenario described.
Thus, the correct inequality that represents this scenario is:
[tex]\[
n(n + 2) < 76
\][/tex]
This inequality captures the relationship described, where the product of two consecutive odd integers is less than 76.
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