https://file.aiquickdraw.com/mathbot/file/1726211749019lpsoxb4p.jpg

The inequality in the image is:

\[
|x| \leq 7
\]

### Solution:

To solve this absolute value inequality, we need to understand that the absolute value expression \( |x| \leq 7 \) means that the value of \( x \) is within 7 units from 0 on the number line.

This can be translated into a compound inequality:

\[
-7 \leq x \leq 7
\]

### Conclusion:

The solution to the inequality \( |x| \leq 7 \) is:

\[
x \in [-7, 7]
\]

### Explanation:

This means that \( x \) can take any value from \(-7\) to \(7\), inclusive.

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Would you like more details or have any questions?

Here are 5 related questions for you:

1. How do you solve inequalities involving absolute values that are greater than a number?
2. What is the geometric interpretation of the absolute value inequality?
3. How would the solution change if the inequality was \( |x| > 7 \)?
4. Can you explain how to solve a more complex absolute value inequality, like \( |2x - 3| \leq 5 \)?
5. What happens when the absolute value is set equal to a negative number?

**Tip:** When solving absolute value inequalities, always consider both the positive and negative scenarios!

Discover how to solve the absolute value inequality |x| < 7 with a clear, step-by-step explanation. This guide covers fundamental concepts such as the definition of absolute values and how to translate them into a simple linear inequality. Suitable for students in Grades 6-9.

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