Find the solution to the inequality x7+13>20 .(1 point) Responses x>49 x greater than 49 x<49 x less than 49 x>1 x greater than 1 x>337

Answer 1

To solve the inequality \( x^7 + 13 > 20 \), we start by isolating the term with \( x \):

1. Subtract 13 from both sides: \[ x^7 > 20 - 13 \] \[ x^7 > 7 \]

2. To solve for \( x \), we take the seventh root of both sides: \[ x > 7^{1/7} \]

3. Since \( 7^{1/7} \) is approximately \( 1.47 \), we can express the solution as: \[ x > 7^{1/7} \]

4. None of the options explicitly state \( x > 7^{1/7} \), but we see that \( 1.47 \) is greater than \( 1 \). Therefore, the best fitting option in the provided responses is:

   • \( x > 1 \)

So the solution to the inequality is \( x > 1 \).