10 The product of -4 and a number is greater than 12 . Which solution from the set makes an inequally represented by the statement true? \[ \left\{-6,-3, r^{-1}, 3,15,16,17\right\} \]

To solve the inequality: \[ -4 \times x > 12 \] 1. **Isolate \( x \):** Divide both sides by \(-4\). Remember, dividing by a negative number reverses the inequality sign: \[ x < \frac{12}{-4} \Rightarrow x < -3 \] 2. **Identify the solutions from the set \(\{-6, -3, r^{-1}, 3, 15, 16, 17\}\) that satisfy \( x < -3 \):** - **\(-6\):** Yes, \(-6 < -3\) - **\(-3\):** No, \(-3\) is not less than \(-3\) - **\(r^{-1}\):** Without additional information about \( r \), we cannot determine if \( r^{-1} < -3 \) - **\(3\), \(15\), \(16\), \(17\):** No, all these values are greater than \(-3\) 3. **Conclusion:** The only definite solution from the set that satisfies the inequality \( x < -3 \) is \(-6\). **Answer:** \(-6\)