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?
A.
Yes, because 31 is equal to 4 ·12-7 .

B.
Yes, because 31 is greater than 4 · 12-7.

C.
No, because 31 is equal to 4 · 12-7 .

D.
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 equation \( 4x - 17 \): \[ 4(12) - 17 = 48 - 17 = 31 \]

2. Now we compare \( y \) with \( 4x - 17 \): \[ 31 \text{ vs } 31 \]

The inequality states \( y > 4x - 17 \), meaning \( y \) must be greater than \( 4x - 17 \) for the point to be a solution. Since \( 31 \) is equal to \( 31 \), it does not satisfy the inequality \( y > 31 \).

Thus, her friend is incorrect. The correct response is:

D. No, because 31 is less than 4 · 12 - 17.