Questions: Put the following inequality in interval notation:
x>17 or x ≤-10
Transcript text: Put the following inequality in interval notation:
\[
x>17 \text { or } x \leq-10
\]
Solution
Solution Steps
To put the given inequality in interval notation, we need to identify the ranges of \( x \) that satisfy each part of the inequality separately and then combine them. The inequality \( x > 17 \) corresponds to the interval \( (17, \infty) \), and the inequality \( x \leq -10 \) corresponds to the interval \( (-\infty, -10] \). The union of these two intervals will give us the final answer.
Step 1: Understand the Inequality
The given inequality is:
\[
x > 17 \text{ or } x \leq -10
\]
This inequality consists of two separate conditions:
\( x > 17 \)
\( x \leq -10 \)
Step 2: Express Each Condition in Interval Notation
First, we express each condition in interval notation:
\( x > 17 \) can be written as \( (17, \infty) \)
\( x \leq -10 \) can be written as \( (-\infty, -10] \)
Step 3: Combine the Intervals
Since the inequality uses "or," we take the union of the two intervals:
\[
(17, \infty) \cup (-\infty, -10]
\]