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?
A) Yes, because 31 is equal to 4 · 12 -17.
B) Yes, because 31 is greater than 4 · 12 -17.
C) No, because 31 is equal to 4 · 12 - 17.
D) No, because 31 is less than 4 · 12 -17.

1 answer

Let's solve the inequality \( y > 4x - 17 \) for the point \( (12, 31) \).

First, substitute \( x = 12 \) into the expression on the right side:

\[ 4x - 17 = 4(12) - 17 \] \[ = 48 - 17 \] \[ = 31 \]

Now, we check the inequality:

The inequality states \( y > 4x - 17 \). In this case, \( y = 31 \) and \( 4x - 17 = 31 \).

Since \( 31 \) is not greater than \( 31 \), but rather equal to \( 31 \), the point does not satisfy the inequality.

Thus, the correct answer is:

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