https://file.aiquickdraw.com/mathbot/file/17261143019534egar01a.jpg

The compound inequality given in the image is:

\[
x \leq 6 \quad \text{or} \quad x \geq 8
\]

To graph this inequality, follow these steps:

1. **For \( x \leq 6 \)**: This indicates all values less than or equal to 6. On the number line, you will plot a closed (filled) circle at 6 because the inequality includes 6 (indicated by the "≤" sign). Then, shade the line to the left of 6 to represent all numbers less than 6.

2. **For \( x \geq 8 \)**: This indicates all values greater than or equal to 8. On the number line, you will plot a closed (filled) circle at 8 because the inequality includes 8 (indicated by the "≥" sign). Then, shade the line to the right of 8 to represent all numbers greater than 8.

### Visual on the Number Line:

- A closed circle at 6 with a shaded line extending to the left.
- A closed circle at 8 with a shaded line extending to the right.

The middle part between 6 and 8 remains unshaded because no values between 6 and 8 satisfy the inequality \(x \leq 6\) or \(x \geq 8\).

Would you like more details or further clarifications? Here are some additional related questions:

1. How do we represent compound inequalities involving "and" versus "or" on a number line?
2. What changes if the inequality was \(x < 6\) instead of \(x \leq 6\)?
3. How do open and closed circles affect the solution on the number line?
4. How would this graph change if there was only one inequality?
5. Can compound inequalities be solved algebraically?

**Tip**: Always pay attention to the inequality symbols. A "≤" or "≥" symbol means the value is included (closed circle), while a "<" or ">" means the value is not included (open circle).

Graph the compound inequality x ≤ 6 or x ≥ 8.

Learn how to graph the compound inequality x ≤ 6 or x ≥ 8. This problem involves understanding compound inequalities and correctly plotting them on a number line. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation