Question

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