https://file.aiquickdraw.com/mathbot/file/173008712648211y4nxpx.jpg

The number line shows values extending left from \(-4\) and right from \(4\), both with closed circles, which suggests an absolute value inequality representing values outside the interval \([-4, 4]\).

To express this in terms of an absolute value inequality, we can set it up as:

\[
|x| \geq 4
\]

### Explanation
This inequality states that the absolute value of \(x\) is greater than or equal to \(4\), covering all numbers that are either \(4\) or more away from \(0\), both in the positive and negative directions.

Would you like further clarification, or do you have additional questions?

### Related Questions
1. How would the inequality change if the circles were open instead of closed?
2. How do you write the solution if it were an inequality without absolute value notation?
3. What does \(|x| \leq 4\) represent on a number line?
4. How can we write compound inequalities to represent intervals on a number line?
5. How do absolute value inequalities apply to real-life situations?

### Tip
When interpreting number lines, closed circles mean the endpoint is included (≥ or ≤), while open circles mean the endpoint is not included (> or <).

Write the absolute value inequality represented here.

Understand how to interpret an absolute value inequality based on a number line representation. This problem involves identifying values outside a specified interval and representing them as an inequality. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation