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 - 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 .

Answer 1

To determine whether the point (12, 31) is a solution to the inequality \(y > 4x - 17\), we first need to substitute \(x = 12\) into the equation and then calculate \(y\).

1. Calculate \(4x - 17\) for \(x = 12\):

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

2. Now, we can evaluate the inequality \(y > 4x - 17\):

Substituting the values, we need to check if \(31 > 31\).

This statement is false because 31 is not greater than 31.

So, the correct answer would be:

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