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?

Answer 1

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

First, we will calculate \(4x - 17\) when \(x = 12\): \[ 4(12) - 17 = 48 - 17 = 31 \]

Now, we can compare \(y\) with \(4x - 17\): Given that \(y = 31\) and \(4x - 17 = 31\), we have: \[ 31 > 31 \]

This is not true because 31 is not greater than 31 (it is equal).

Thus, since \(y\) must be strictly greater than \(4x - 17\) to satisfy the inequality \(y > 4x - 17\), the point (12, 31) does not satisfy the inequality.

Therefore, her friend is not correct.