Question
A student wrote the inequality y>4x-17. Her friend solved the inequality and said that (12,31) is one of the possible solutions of this inequality. Is her friend correct?(1 point) Responses No, because 31 is less than 4 · 12-17. No, because 31 is less than 4 · 12-17. Yes, because 31 is equal to 4 · 12-17. Yes, because 31 is equal to 4 · 12-17. No, because 31 is equal to 4 · 12-17. No, because 31 is equal to 4 · 12-17. Yes, because 31 is greater than 4 · 12-17.
Answers
GPT-4o mini
To determine if the point (12, 31) is a solution to the inequality \( y > 4x - 17 \), we first need to evaluate the right side of the inequality at \( x = 12 \):
\[
4(12) - 17 = 48 - 17 = 31
\]
Now we can check the inequality:
- The inequality is \( y > 4x - 17 \).
- For \( x = 12 \), we found \( 4(12) - 17 = 31 \).
- The point is \( (12, 31) \), which gives \( y = 31 \).
Since we need \( y \) to be **greater** than \( 31 \) (as per the inequality \( y > 31 \)), the friend is incorrect, because \( 31 \) is not greater than \( 31\); it is equal to it.
Therefore, the correct response is:
**No, because 31 is equal to 4 · 12 - 17.**
\[
4(12) - 17 = 48 - 17 = 31
\]
Now we can check the inequality:
- The inequality is \( y > 4x - 17 \).
- For \( x = 12 \), we found \( 4(12) - 17 = 31 \).
- The point is \( (12, 31) \), which gives \( y = 31 \).
Since we need \( y \) to be **greater** than \( 31 \) (as per the inequality \( y > 31 \)), the friend is incorrect, because \( 31 \) is not greater than \( 31\); it is equal to it.
Therefore, the correct response is:
**No, because 31 is equal to 4 · 12 - 17.**