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.

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!