Questions: Put the following inequality in interval notation: x>17 or x ≤-10

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.

The given inequality is: \[ x > 17 \text{ or } x \leq -10 \]

This inequality consists of two separate conditions:

1. \( x > 17 \)
2. \( x \leq -10 \)

First, we express each condition in interval notation:

1. \( x > 17 \) can be written as \( (17, \infty) \)
2. \( x \leq -10 \) can be written as \( (-\infty, -10] \)

Since the inequality uses "or," we take the union of the two intervals: \[ (17, \infty) \cup (-\infty, -10] \]

Final Answer