Question
Which of the following values for n makes the inequality 2n−−√<5 true?
8
16
18
12.5
8
16
18
12.5
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the inequality \( \sqrt{2n} < 5 \), we can first square both sides to eliminate the square root (as long as we know both sides are non-negative):
\[
2n < 25
\]
Next, we divide both sides by 2 to isolate \( n \):
\[
n < 12.5
\]
Now we can evaluate the options given:
- **8**: \( 8 < 12.5 \) (True)
- **16**: \( 16 < 12.5 \) (False)
- **18**: \( 18 < 12.5 \) (False)
- **12.5**: \( 12.5 < 12.5 \) (False)
The only value for \( n \) that makes the inequality true is:
**8**.
\[
2n < 25
\]
Next, we divide both sides by 2 to isolate \( n \):
\[
n < 12.5
\]
Now we can evaluate the options given:
- **8**: \( 8 < 12.5 \) (True)
- **16**: \( 16 < 12.5 \) (False)
- **18**: \( 18 < 12.5 \) (False)
- **12.5**: \( 12.5 < 12.5 \) (False)
The only value for \( n \) that makes the inequality true is:
**8**.
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