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 Yes, because 31 is greater than 4 · 12-17. Yes, because 31 is greater 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 less than 4 · 12-17. No, because 31 is less than 4 · 12-17. No, because 31 is equal to 4 · 12-17. No, because 31 is equal to 4 · 12-17.

Answer 1

To determine if (12, 31) is a solution to the inequality \( y > 4x - 17 \), we need to substitute \( x = 12 \) into the inequality and see if \( y = 31 \) satisfies it.

First, calculate \( 4 \cdot 12 - 17 \):

\[
4 \cdot 12 = 48
\]
\[
48 - 17 = 31
\]

So, we have:

\[
y > 31
\]

Since \( 31 \) is not greater than \( 31 \), the inequality is not satisfied by \( y = 31 \).

Therefore, the answer is:

**No, because 31 is equal to 4 · 12 - 17.**