Question
Which of the following values for n makes the inequality 2n−−√<5 true?(1 point)
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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, we must ensure that both sides are non-negative when doing so.
1. Start with the inequality:
\[
\sqrt{2n} < 5
\]
2. Square both sides:
\[
2n < 25
\]
3. Now, divide both sides by 2 to isolate \( n \):
\[
n < \frac{25}{2}
\]
\[
n < 12.5
\]
Thus, the inequality \( \sqrt{2n} < 5 \) is true for values of \( n \) that are less than 12.5.
If you want a specific integer or natural number value for \( n \), any integer less than or equal to 12 would satisfy this inequality (e.g., \( n = 0, 1, 2, \ldots, 12 \)).
1. Start with the inequality:
\[
\sqrt{2n} < 5
\]
2. Square both sides:
\[
2n < 25
\]
3. Now, divide both sides by 2 to isolate \( n \):
\[
n < \frac{25}{2}
\]
\[
n < 12.5
\]
Thus, the inequality \( \sqrt{2n} < 5 \) is true for values of \( n \) that are less than 12.5.
If you want a specific integer or natural number value for \( n \), any integer less than or equal to 12 would satisfy this inequality (e.g., \( n = 0, 1, 2, \ldots, 12 \)).
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