Which Number Line Represents The Solution Set For The Inequality $3x \ \textless \ -9$?

**Which Number Line Represents the Solution Set for the Inequality $3x \ \textless \ -9$?**

Understanding the Inequality

The given inequality is $3x \ \textless \ -9$. To find the solution set, we need to isolate the variable $x$. This can be done by dividing both sides of the inequality by $3$. However, when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes.

Step 1: Divide Both Sides by 3

To isolate $x$, we divide both sides of the inequality by $3$. However, since we are dividing by a negative number, we need to change the direction of the inequality sign.

$$\frac{3x}{3} \ \textless \ \frac{-9}{3}$$

This simplifies to:

$$x \ \textless \ -3$$

Step 2: Understanding the Solution Set

The solution set for the inequality $x \ \textless \ -3$ represents all the values of $x$ that satisfy the inequality. Since $x$ is less than $-3$, the solution set includes all real numbers less than $-3$.

Which Number Line Represents the Solution Set?

To represent the solution set on a number line, we need to shade the region that includes all real numbers less than $-3$. The number line should have a closed circle at $-3$ to indicate that $-3$ is not included in the solution set.

Q&A

Q: What is the solution set for the inequality $3x \ \textless \ -9$?

A: The solution set for the inequality $3x \ \textless \ -9$ is all real numbers less than $-3$.

Q: How do I represent the solution set on a number line?

A: To represent the solution set on a number line, you need to shade the region that includes all real numbers less than $-3$. The number line should have a closed circle at $-3$ to indicate that $-3$ is not included in the solution set.

Q: What happens when we divide an inequality by a negative number?

A: When we divide an inequality by a negative number, the direction of the inequality sign changes.

Q: Can I include $-3$ in the solution set?

A: No, $-3$ is not included in the solution set. The solution set includes all real numbers less than $-3$.

Q: How do I know if the solution set is open or closed?

A: The solution set is open because it includes all real numbers less than $-3$, but does not include $-3$ itself.

Conclusion

In conclusion, the solution set for the inequality $3x \ \textless \ -9$ is all real numbers less than $-3$. To represent the solution set on a number line, you need to shade the region that includes all real numbers less than $-3$. The number line should have a closed circle at $-3$ to indicate that $-3$ is not included in the solution set.

Frequently Asked Questions

• Q: What is the solution set for the inequality $3x \ \textless \ -9$? A: The solution set for the inequality $3x \ \textless \ -9$ is all real numbers less than $-3$.
• Q: How do I represent the solution set on a number line? A: To represent the solution set on a number line, you need to shade the region that includes all real numbers less than $-3$. The number line should have a closed circle at $-3$ to indicate that $-3$ is not included in the solution set.
• Q: What happens when we divide an inequality by a negative number? A: When we divide an inequality by a negative number, the direction of the inequality sign changes.
• Q: Can I include $-3$ in the solution set? A: No, $-3$ is not included in the solution set. The solution set includes all real numbers less than $-3$.
• Q: How do I know if the solution set is open or closed? A: The solution set is open because it includes all real numbers less than $-3$, but does not include $-3$ itself.

Additional Resources

• Inequality Basics: Learn the basics of inequalities and how to solve them.
• Number Line Basics: Learn how to represent solution sets on a number line.
• Algebra Basics: Learn the basics of algebra and how to solve equations and inequalities.