If the replacement set is the set of integers, find the solution set for the inequality:

Question

x-9 < -15

Answer 1

To solve the inequality \( x - 9 < -15 \), follow these steps:

1. Add 9 to both sides of the inequality to isolate \( x \): \[ x - 9 + 9 < -15 + 9 \] This simplifies to: \[ x < -6 \]

2. Identify the solution set: Since the replacement set is the set of integers, the solution set consists of all integers less than \(-6\).

Thus, the solution set is: \[ { \ldots, -8, -7 } \] This can also be represented using interval notation as \( (-\infty, -6) \) when considering all integers.