Question
If the replacement set is the set of integers find the solution set for the inequality x-9<15
Answers
GPT-4o mini
To solve the inequality \( x - 9 < 15 \), follow these steps:
1. **Add 9 to both sides** of the inequality:
\[
x - 9 + 9 < 15 + 9
\]
This simplifies to:
\[
x < 24
\]
2. **Determine the solution set**: Since the replacement set is the set of integers, the solution set will consist of all integers that are less than 24.
Thus, the solution set is:
\[
\{ \ldots, -3, -2, -1, 0, 1, 2, 3, \ldots, 23 \}
\]
In interval notation, this can be expressed as:
\[
(-\infty, 24)
\]
However, specifically for integers, you can list them as \( \{ x \in \mathbb{Z} \mid x < 24 \} \).
1. **Add 9 to both sides** of the inequality:
\[
x - 9 + 9 < 15 + 9
\]
This simplifies to:
\[
x < 24
\]
2. **Determine the solution set**: Since the replacement set is the set of integers, the solution set will consist of all integers that are less than 24.
Thus, the solution set is:
\[
\{ \ldots, -3, -2, -1, 0, 1, 2, 3, \ldots, 23 \}
\]
In interval notation, this can be expressed as:
\[
(-\infty, 24)
\]
However, specifically for integers, you can list them as \( \{ x \in \mathbb{Z} \mid x < 24 \} \).