To solve the inequality \( \sqrt{2n} < 5 \), we can first square both sides (assuming \( n \) is non-negative, since we're dealing with a square root):
\[ 2n < 25 \]
Now, divide both sides by 2:
\[ n < 12.5 \]
Now we can evaluate the given options:
a) \( n = 8 \): \( 8 < 12.5 \) (True)
b) \( n = 12.5 \): \( 12.5 < 12.5 \) (False)
c) \( n = 16 \): \( 16 < 12.5 \) (False)
d) \( n = 18 \): \( 18 < 12.5 \) (False)
The only value of \( n \) that satisfies the inequality \( \sqrt{2n} < 5 \) is:
a) 8