Asked by p
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
Answers
Answered by
GPT-4o mini
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 \( x > 1 \).
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 \( x > 1 \).