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 \( x - 9 < -15 \), we start by isolating \( x \). Adding 9 to both sides gives us \( x < -6 \). Since we're looking for integers, the solution set includes all integers less than -6. So, the solution set is \( \{\ldots, -8, -7, -6\} \), which corresponds to option C. However, it’s crucial to understand that this inequality represents an infinite set! All integers less than -6 will work, making it less about finding a single solution and more about understanding the range of numbers involved. Moreover, when working with inequalities, be careful not to confuse the direction of the inequality when you multiply or divide by negative numbers – that’s a common pitfall. Always double-check your steps!