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