Express the interval using two different representations.
left parenthesis, minus, infinity, comma, minus, 8, right parenthesis, union, left parenthesis, minus, 3, comma, infinity, right parenthesis
(−∞,−8)∪(−3,∞)
Answer
Attempt 1 out of 2

           
Inequality Notation:   
Number Line:
Click and drag to plot line.
-12
-10
-8
-6
-4
-2
0
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The interval \((-\infty, -8) \cup (-3, \infty)\) can be represented in two different forms:

### 1. **Inequality Notation**
This interval can be broken into two parts:
- For the left part, \( x < -8 \).
- For the right part, \( x > -3 \).

So, the inequality notation for this interval is:
\[
x < -8 \quad \text{or} \quad x > -3.
\]

### 2. **Number Line Representation**
To represent this on a number line:
- Draw an open circle at \(-8\) and shade everything to the left (indicating values less than \(-8\)).
- Draw an open circle at \(-3\) and shade everything to the right (indicating values greater than \(-3\)).

### Do you want more details or have any questions?

### 5 Related Questions
1. How would the interval \((-5, 7]\) be expressed in inequality notation?
2. What is the difference between an open interval and a closed interval on a number line?
3. How would the interval \([-2, 5) \cup (6, \infty)\) be expressed using inequality notation?
4. How do we represent an interval with closed boundaries (e.g., \([-1, 4]\)) on a number line?
5. How would \((-\infty, -8] \cup [-3, \infty)\) differ in inequality notation from the interval given?

### Tip
Open intervals (like \( (a, b) \)) do not include the endpoints, whereas closed intervals (like \( [a, b] \)) do include the endpoints.

Express the interval using two different representations. (−∞,−8)∪(−3,∞)

Learn how to express the interval (−∞,−8)∪(−3,∞) using inequality notation and a number line. This math problem focuses on key concepts such as inequalities, interval notation, and visualizing intervals on a number line. Ideal for high school students in Grades 9-12.

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