To represent the compound inequality $-1 \leq x \leq 5$ using absolute value, you can express it as:

$|x - 2| \leq 3$

Explanation:

1. The midpoint between $-1$ and $5$ is $2$. This midpoint helps center the absolute value expression.
2. The distance from $2$ to either $-1$ or $5$ is $3$, which becomes the boundary for the inequality.

Thus, $|x - 2| \leq 3$ captures all the values of $x$ between $-1$ and $5$, inclusive.

Would you like a more detailed explanation or have any questions?

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Here are 5 related questions you might want to explore:

1. How do you solve an absolute value inequality like $|x - 2| \leq 3$?
2. What is the geometric interpretation of absolute value inequalities?
3. How do you convert a compound inequality like $-4 \leq x \leq 6$ into an absolute value inequality?
4. What changes if the inequality was $-1 < x < 5$ instead of including the endpoints?
5. How do you solve absolute value inequalities with strict inequalities (e.g., $|x - 2| < 3$)?

Tip: Absolute value inequalities are often used to describe ranges of values that lie within a certain distance from a central point.