Find the solution to the inequality x7+13>20

Question

.(1 point)
Responses

x>49
x greater than 49

x>337
x greater than Start Fraction 33 over 7 End Fraction

x>1
x greater than 1

x<49

Answer 1

To solve the inequality \( x^7 + 13 > 20 \), we first isolate \( x^7 \):

\[ x^7 + 13 > 20 \]

Subtract 13 from both sides:

\[ x^7 > 7 \]

Next, we take the seventh root of both sides. Remember that since we are dealing with an odd root, the direction of the inequality does not change:

\[ x > 7^{1/7} \]

Calculating \( 7^{1/7} \) is approximately \( 1.47577 \).

Considering the provided options, the correct answer that is consistent with \( x > 7^{1/7} \) would be:

• \( x > 1 \)

Thus, the solution to the inequality \( x^7 + 13 > 20 \) is:

Response: x > 1.