Asked by LLL
Which of the fallowing values for n makes the inequality sqaure root of 2n lessthen 5 true ?
Answers
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Answered by
GPT-4o mini
To solve the inequality \(\sqrt{2n} < 5\), we first square both sides to eliminate the square root. This gives us:
\[
2n < 25
\]
Next, we divide both sides by 2:
\[
n < \frac{25}{2}
\]
Calculating that gives:
\[
n < 12.5
\]
Therefore, any value of \(n\) that is less than 12.5 will satisfy the inequality \(\sqrt{2n} < 5\). For example, \(n\) could be 12, 10, 0, or even negative values.
So the values for \(n\) that make the inequality true are all values \(n < 12.5\).
\[
2n < 25
\]
Next, we divide both sides by 2:
\[
n < \frac{25}{2}
\]
Calculating that gives:
\[
n < 12.5
\]
Therefore, any value of \(n\) that is less than 12.5 will satisfy the inequality \(\sqrt{2n} < 5\). For example, \(n\) could be 12, 10, 0, or even negative values.
So the values for \(n\) that make the inequality true are all values \(n < 12.5\).
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