Solve the absolute value inequality. Graph the solution set.|10x|<-3. write the answer in interval notation

The inequality given is:

\[
|10x| < -3
\]

### Step 1: Analyze the Inequality
Absolute value expressions represent the distance from zero, which is always non-negative. This means:

\[
|10x| \geq 0
\]

Since \(|10x|\) is always greater than or equal to 0, it **cannot** be less than \(-3\), because \(-3\) is negative. There is no value of \(x\) that would satisfy this inequality.

### Conclusion
Since the inequality has no solutions, the solution set is empty.

### Answer in Interval Notation
The solution set in interval notation is:

\[
\emptyset
\]

### Graph
The graph of the solution set would also be empty, as there are no values of \(x\) that satisfy this inequality.

Would you like more details or have any questions?

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### Related Questions

1. How would you solve and graph the inequality \( |x + 2| < 5 \)?
2. What are the steps to solve an absolute value inequality of the form \( |ax + b| > c \)?
3. Can an absolute value expression ever be negative? Why or why not?
4. What does it mean when an absolute value inequality has an empty solution set?
5. How would the inequality change if it were \( |10x| > 3 \) instead?

### Tip
For absolute value inequalities, remember that \( |A| < B \) implies \( -B < A < B \), but only when \( B \geq 0 \).

Solve the absolute value inequality. Graph the solution set. |10x| < -3. Write the answer in interval notation.

Learn how to solve the absolute value inequality |10x| < -3 and understand why the solution set is empty. This problem demonstrates the absolute value theorem, explaining why an absolute value cannot be less than a negative number, making it suitable for students in Grades 9-11.

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