Question

Solve x13<45
.(1 point)
Responses

x>525
x greater than Start Fraction 52 over 5 End Fraction

x<1025
x less than 10 Start Fraction 2 over 5 End Fraction

x<1345
x less than 13 Start Fraction 4 over 5 End Fraction

x<465

Answer 1

To solve the inequality \( x^{13} < 45 \), we first need to isolate \( x \).

1. Taking the 13th root of both sides gives:
\[
x < 45^{\frac{1}{13}}
\]

2. Now, we will approximate \( 45^{\frac{1}{13}} \):

Using a calculator, we find that:
\[
45^{\frac{1}{13}} \approx 1.4678
\]

3. Since we need \( x \) to be less than this value, we can write:
\[
x < 1.4678
\]

Now, let’s convert \( 45^{\frac{1}{13}} \) to a fraction. The exact value of \( 45^{\frac{1}{13}} \) is not exactly represented in simple fractions.

Looking at the provided options, we can analyze them:

- \( x > 525 \)
- \( x < \frac{52}{5} = 10.4 \)
- \( x < \frac{1345}{100} = 13.45 \)
- \( x < 465 \)

Since \( 1.4678 \) is less than all these fractions except \( 52/5 \).

Thus, the valid response is:
\[
x < \frac{52}{5}
\]
which represents the solution \( x < 10.4 \).

In conclusion, the correct option is:
**x < \frac{52}{5}**.