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The inequality given is \( |y| \leq 8 \), which means we need to find all values of \( y \) such that the absolute value of \( y \) is less than or equal to 8.

To solve this:

1. We rewrite the absolute value inequality \( |y| \leq 8 \) as a compound inequality:
   \[
   -8 \leq y \leq 8
   \]
   This means \( y \) can be any number between -8 and 8, inclusive.

2. To graph this on a number line:
   - Place solid dots at \( -8 \) and \( 8 \) because the inequality includes the endpoints (indicated by \( \leq \)).
   - Shade the region between \( -8 \) and \( 8 \), including all the numbers in this range.

This is how the graph would look:
- The number line extends from \( -10 \) to \( 10 \).
- Solid dots at \( -8 \) and \( 8 \).
- A shaded line between \( -8 \) and \( 8 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you solve absolute value inequalities with \( \geq \) instead of \( \leq \)?
2. How can you solve an absolute value inequality like \( |y + 3| \leq 5 \)?
3. What happens if the inequality is \( |y| > 8 \) instead of \( \leq 8 \)?
4. Can absolute value inequalities have no solution?
5. How does the solution change if the absolute value inequality includes a negative number?

**Tip**: For absolute value inequalities, if you have \( |x| \leq a \), always remember this means \( -a \leq x \leq a \).

Graph the solution to the inequality |y| ≤ 8 on the number line.

Learn how to graph the solution of the absolute value inequality |y| ≤ 8. This algebraic concept covers key steps including rewriting the inequality as -8 ≤ y ≤ 8, placing solid points at -8 and 8, and shading the region between them on a number line.

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