QuestionExpress the interval $(-\infty,-9) \cup(0, \infty)$ using inequalities.

Studdy Solution

STEP 1

Assumptions1. The given interval is $(-\infty,-9) \cup(0, \infty)$ . The notation $(a, b)$ represents all numbers between $a$ and $b$ , not including $a$ and $b$ themselves3. The notation $(-\infty, a)$ represents all numbers less than $a$
4. The notation $(a, \infty)$ represents all numbers greater than $a$
5. The symbol $\cup$ represents the union of two sets, meaning all elements that are in either set

STEP 2

We need to express the given interval using inequality notation. The interval $(-\infty,-9)$ represents all numbers less than $-9$ , and $(0, \infty)$ represents all numbers greater than $0$ .
So, we can write the interval as $x < -9 \quad or \quad x >0$

STEP 3

In mathematics, the word "or" is often represented by the symbol $\cup$ . So, we can also write the interval as $x < -9 \cup x >0$ This is the inequality notation for the given interval.

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