If the replacement set is the set of integers, find the solution set for the inequality: \( x-9<-15 \) A \( \{-8,-7,-6, \ldots\} \) B \( \{-9,-8,-7, \ldots\} \) C \( \{\ldots,-8,-7,-6\} \) D \( \{\ldots,-9,-8,-7\} \)

To solve the inequality \( x - 9 < -15 \): 1. **Isolate \( x \):** \[ x - 9 < -15 \\ x < -15 + 9 \\ x < -6 \] 2. **Determine the Solution Set:** - Since \( x \) must be less than \(-6\) and the replacement set is the set of integers, the solution includes all integers **less than** \(-6\). - This means the integers \(-7, -8, -9, \ldots\) are part of the solution set. 3. **Match with Given Options:** - **Option D**: \( \{\ldots, -9, -8, -7\} \) correctly represents all integers less than \(-6\). **Answer:** **D \( \{\ldots,-9,-8,-7\} \)**