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.

Question

Is her friend correct?

Answer 1

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

First, calculate \( 4x - 17 \) when \( x = 12 \):

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

Now we can substitute \( x = 12 \) and \( y = 31 \) into the inequality:

\[ 31 > 31 \]

This statement is false because 31 is not greater than 31; they are equal.

Since the point (12, 31) does not satisfy the inequality \( y > 4x - 17 \), her friend is incorrect.