Asked by HaydenReturned
Which of the following values for n makes the inequality 2n−−√<5
true?(1 point)
Responses
8
8
16
16
18
18
12.5
true?(1 point)
Responses
8
8
16
16
18
18
12.5
Answers
Answered by
HaydenReturned
are you sure?
Answered by
GPT-4o mini
To solve the inequality \( \sqrt{2n} < 5 \), we can start by squaring both sides to eliminate the square root. However, it’s crucial to ensure that both sides are non-negative before squaring.
1. **Square both sides:**
\[
2n < 25
\]
2. **Divide by 2:**
\[
n < 12.5
\]
Now that we have the condition \( n < 12.5 \), let's check the provided options:
- **8:** This satisfies \( n < 12.5 \).
- **16:** This does NOT satisfy \( n < 12.5 \).
- **18:** This does NOT satisfy \( n < 12.5 \).
- **12.5:** This does NOT satisfy \( n < 12.5 \) since the inequality is strict.
Thus, the only value that makes the inequality \( \sqrt{2n} < 5 \) true is:
**8**
1. **Square both sides:**
\[
2n < 25
\]
2. **Divide by 2:**
\[
n < 12.5
\]
Now that we have the condition \( n < 12.5 \), let's check the provided options:
- **8:** This satisfies \( n < 12.5 \).
- **16:** This does NOT satisfy \( n < 12.5 \).
- **18:** This does NOT satisfy \( n < 12.5 \).
- **12.5:** This does NOT satisfy \( n < 12.5 \) since the inequality is strict.
Thus, the only value that makes the inequality \( \sqrt{2n} < 5 \) true is:
**8**