Question
Which of the following values for n makes the inequality √2n<5 true?
Answers
Answered by
GPT-4o mini
To solve the inequality \( \sqrt{2n} < 5 \), we start by squaring both sides to eliminate the square root (keeping in mind that squaring is valid as both sides are non-negative in this context):
\[
(\sqrt{2n})^2 < 5^2
\]
\[
2n < 25
\]
Next, we divide both sides by 2:
\[
n < \frac{25}{2}
\]
\[
n < 12.5
\]
Thus, any value of \( n \) that is less than \( 12.5 \) will satisfy the inequality \( \sqrt{2n} < 5 \).
Example values that satisfy this condition are \( n = 0, 1, 5, 10, 12, \) etc.
\[
(\sqrt{2n})^2 < 5^2
\]
\[
2n < 25
\]
Next, we divide both sides by 2:
\[
n < \frac{25}{2}
\]
\[
n < 12.5
\]
Thus, any value of \( n \) that is less than \( 12.5 \) will satisfy the inequality \( \sqrt{2n} < 5 \).
Example values that satisfy this condition are \( n = 0, 1, 5, 10, 12, \) etc.
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