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

1 answer

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 check if \(y = 31\) satisfies it.

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

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

The inequality is:

\[ y > 4x - 17 \implies y > 31 \]

Since \(y = 31\) at the point (12, 31), it does not satisfy the inequality \(y > 31\). Thus, her friend is not correct.

The correct choice is:

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

(Note: Here, "less than" may seem misleading since \(31\) is actually equal to \(4(12) - 17\); hence, the statement should more accurately reflect 'not greater than'.)