Question

Which of the following values for n makes the inequality 2n−−√<5
true?(1 point)
Responses

12.5
12.5

18
18

16
16

8

Answer 1

Which equation matches the solution set of {5}
?(1 point)
Responses

x+x−9=1+x
x plus x minus 9 equals 1 plus x

x^2−10=15
x squared minus 10 equals 15

3x/5+4=7
Start Fraction 3 x over 5 End Fraction plus 4 equals 7

2x−20=30

Answer 2

To solve the inequality \( \sqrt{2n} < 5 \), we can first square both sides to eliminate the square root. However, we need to ensure that we are considering the non-negative values since the square root function is defined for non-negative numbers.

Starting with the inequality:

\[
\sqrt{2n} < 5
\]

Squaring both sides gives:

\[
2n < 25
\]

Now, divide both sides by 2:

\[
n < 12.5
\]

Now let's evaluate the given options to see which values of \( n \) satisfy \( n < 12.5 \):

1. **12.5**: This does not satisfy the inequality since we want \( n < 12.5 \).
2. **18**: This does not satisfy the inequality since \( 18 > 12.5 \).
3. **16**: This does not satisfy the inequality since \( 16 > 12.5 \).
4. **8**: This satisfies the inequality since \( 8 < 12.5 \).

The value that makes the inequality true is **8**.