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отметь на координатной прямой множество решений неравенства

The inequality given is:

\[
|x| < 4
\]

This inequality means that the absolute value of \( x \) is less than 4. To solve this, we consider the definition of absolute value:

\[
|x| < 4 \implies -4 < x < 4
\]

### Solution on the Number Line:

To represent this solution on the number line:

1. Draw a number line with marks at -4, 0, and 4.
2. Place open circles (to indicate that -4 and 4 are not included) at -4 and 4.
3. Shade the region between -4 and 4.

This shaded region represents all values of \( x \) that satisfy the inequality \(|x| < 4\).

Would you like more details, or do you have any questions?

### Relative Questions to Explore:

1. What does the absolute value of a number represent?
2. How do you solve inequalities involving absolute values with greater than (\(>\)) signs?
3. What is the difference between open and closed circles on a number line?
4. How do you represent compound inequalities on a number line?
5. How can we solve inequalities involving absolute values with more complex expressions?

**Tip:** When solving absolute value inequalities, always consider the two possible cases (positive and negative scenarios) for a comprehensive solution.

Explore how to graphically represent the inequality |x| < 4 on a number line. Understand the concept of absolute value and its application in inequalities. Suitable for Grades 9-12.

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