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?

Question

A. No, because 31 is equel to 4 ⋅ 12 - 17
B. No, because 31 is less than 4 ⋅ 12 - 7

Answer 1

To determine if the point (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.

1. Substitute \( x = 12 \) into the expression \( 4x - 17 \): \[ 4(12) - 17 = 48 - 17 = 31 \]

2. Now we have: \[ y > 31 \]

3. Since \( 31 \) is not greater than \( 31 \), the point (12, 31) does not satisfy the inequality \( y > 4x - 17 \).

Therefore, we can conclude that the friend is incorrect. The correct reason among the given options is:

A. No, because 31 is equal to 4 ⋅ 12 - 17.