Choose the correct interval notation for the inequality notation
−3 < x ≤ 3 or 7 ≤ x

(-3, 3] ⋃ [7, ∞)

(-3, 3) ⋃ (7, ∞)

[-3, 3) ⋃ [7, ∞)

[-3, 3] ⋃ (7, ∞)
None of these

Let's break down the inequality to find the correct interval notation.

The inequality is:

\[
-3 < x \leq 3 \quad \text{or} \quad 7 \leq x
\]

### First part: \(-3 < x \leq 3\)
This translates to the interval:
\[
(-3, 3]
\]
- Parentheses for \(-3\) because it is not included.
- Bracket for \(3\) because it is included.

### Second part: \(7 \leq x\)
This translates to the interval:
\[
[7, \infty)
\]
- Bracket for \(7\) because it is included.
- Parentheses for \(\infty\) because \(\infty\) is not a number and can't be included.

Now, combining both parts with the union symbol (\(\cup\)), the correct interval notation is:
\[
(-3, 3] \cup [7, \infty)
\]

### Conclusion:
The correct option is:
\[
(-3, 3] \cup [7, \infty)
\]

Do you want more details or have any other questions? Here are some related problems:

1. What is the interval notation for \(x > -2\) and \(x \leq 4\)?
2. How do we express \(x < 0\) or \(x \geq 5\) in interval notation?
3. Convert \(1 \leq x < 10\) to interval notation.
4. Solve and express \(x > 3\) and \(x \leq 8\) in interval notation.
5. How would you graph the inequality \(x \geq 2\) on a number line?

**Tip**: Always remember that parentheses \(()\) mean the endpoint is excluded, while brackets \([]\) mean the endpoint is included!

Choose the correct interval notation for the inequality notation −3 < x ≤ 3 or 7 ≤ x

Learn how to write the correct interval notation for the inequality −3 < x ≤ 3 or 7 ≤ x. This problem involves understanding inequalities and interval notation, combining intervals using the union symbol. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation