Question

Solve x9<2
.(1 point)
Responses

x>11
x greater than 11

x<18
x less than 18

x<11
x less than 11

x<29

Answer 1

To solve the inequality \( x^9 < 2 \), we can first take the ninth root of both sides.

Taking the ninth root gives us:

\[
x < 2^{1/9}
\]

Now we can calculate \( 2^{1/9} \):

Using a calculator, \( 2^{1/9} \) is approximately \( 1.0801 \).

This tells us that:

\[
x < 1.0801
\]

Now, let's evaluate the answer choices provided:

- **x > 11**: This is false.
- **x < 18**: This is true, but not the best answer.
- **x < 11**: This is true, but again not the best answer based on our calculation.
- **x < 29**: This is also true, but not specific.

The most precise answer should be:

**x < 2^{1/9}**.

However, since that exact answer is not among the options, the most restrictive and relevant option based on the provided answers would be:

**x < 11**.

So the best response that fits the inequality is:

**x < 11**.