Question

which of the following is a solution to the inequality below?
-17 > \frac{51}{y}

options: y = 3, y = 1, y = -3, y = -1

Explanation:

Step1: Test \( y = 3 \)

Substitute \( y = 3 \) into \( \frac{51}{y} \), we get \( \frac{51}{3}=17 \). Now check \( -17>17 \)? No, because \( -17 < 17 \).

Step2: Test \( y = 1 \)

Substitute \( y = 1 \) into \( \frac{51}{y} \), we get \( \frac{51}{1}=51 \). Check \( -17>51 \)? No, \( -17 < 51 \).

Step3: Test \( y = - 3 \)

Substitute \( y=-3 \) into \( \frac{51}{y} \), we get \( \frac{51}{-3}=-17 \). Check \( -17>-17 \)? No, because \( -17 = -17 \), and the inequality is strict (\(>\), not \( \geq \)).

Step4: Test \( y=-1 \)

Substitute \( y = - 1 \) into \( \frac{51}{y} \), we get \( \frac{51}{-1}=-51 \). Check \( -17>-51 \)? Yes, because when comparing two negative numbers, the one with the smaller absolute value is larger. \(|-17| = 17\), \(|-51|=51\), and \(17<51\), so \( - 17>-51\).

Answer:

\( y = -1 \)