Solve For V V V And Graph The Solution. − 10 ≤ 3 V − 2 2 \textless 8 -10 \leq \frac{3v-2}{2} \ \textless \ 8 − 10 ≤ 2 3 V − 2 ​ \textless 8 Plot The Endpoints. Select An Endpoint To Change It From Closed To Open. Select The Middle Of A Segment, Ray, Or Line To Delete It.

Introduction

Inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to. Solving and graphing inequalities is an essential skill in mathematics, and it requires a clear understanding of the concepts and techniques involved. In this article, we will focus on solving and graphing the inequality $-10 \leq \frac{3v-2}{2} \ \textless \ 8$.

Understanding the Inequality

The given inequality is a compound inequality, which means it consists of two parts: $-10 \leq \frac{3v-2}{2}$ and $\frac{3v-2}{2} \ \textless \ 8$. To solve this inequality, we need to isolate the variable $v$ and find the values that satisfy both parts.

Step 1: Multiply Both Sides by 2

The first step in solving the inequality is to multiply both sides by 2 to eliminate the fraction. This gives us:

$$-20 \leq 3v-2 \ \textless \ 16$$

Step 2: Add 2 to Both Sides

Next, we add 2 to both sides of the inequality to isolate the term with the variable $v$. This gives us:

$$-18 \leq 3v \ \textless \ 18$$

Step 3: Divide Both Sides by 3

Finally, we divide both sides of the inequality by 3 to solve for $v$. This gives us:

$$-6 \leq v \ \textless \ 6$$

Graphing the Solution

To graph the solution, we need to plot the endpoints of the inequality on a number line. The endpoints are $-6$ and $6$, which are the values that satisfy the inequality.

Plotting the Endpoints

To plot the endpoints, we need to place a point on the number line at each endpoint. The point at $-6$ is an open circle, and the point at $6$ is a closed circle.

Selecting an Endpoint

To change the inequality from closed to open, we need to select one of the endpoints and change it from a closed circle to an open circle. Let's select the endpoint at $-6$ and change it from a closed circle to an open circle.

Deleting a Segment

To delete a segment, ray, or line, we need to select the middle of the segment, ray, or line and delete it. Let's select the middle of the segment between $-6$ and $6$ and delete it.

Conclusion

Solving and graphing inequalities is an essential skill in mathematics, and it requires a clear understanding of the concepts and techniques involved. In this article, we focused on solving and graphing the inequality $-10 \leq \frac{3v-2}{2} \ \textless \ 8$. We used the steps of multiplying both sides by 2, adding 2 to both sides, and dividing both sides by 3 to solve for $v$. We also graphed the solution by plotting the endpoints on a number line and selecting an endpoint to change it from closed to open. Finally, we deleted a segment, ray, or line by selecting the middle of the segment, ray, or line and deleting it.

Tips and Tricks

• When solving inequalities, always start by isolating the variable on one side of the inequality.
• When graphing inequalities, always plot the endpoints on a number line.
• When changing an inequality from closed to open, always select one of the endpoints and change it from a closed circle to an open circle.
• When deleting a segment, ray, or line, always select the middle of the segment, ray, or line and delete it.

Common Mistakes

• Failing to isolate the variable on one side of the inequality.
• Failing to plot the endpoints on a number line.
• Failing to change an endpoint from closed to open when changing an inequality from closed to open.
• Failing to delete a segment, ray, or line by selecting the middle of the segment, ray, or line and deleting it.

Real-World Applications

Solving and graphing inequalities has many real-world applications, including:

• Finance: In finance, inequalities are used to model financial transactions and investments.
• Science: In science, inequalities are used to model physical phenomena and predict outcomes.
• Engineering: In engineering, inequalities are used to design and optimize systems.
• Computer Science: In computer science, inequalities are used to model algorithms and data structures.

Conclusion

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Introduction

In our previous article, we discussed solving and graphing the inequality $-10 \leq \frac{3v-2}{2} \ \textless \ 8$. We used the steps of multiplying both sides by 2, adding 2 to both sides, and dividing both sides by 3 to solve for $v$. We also graphed the solution by plotting the endpoints on a number line and selecting an endpoint to change it from closed to open. In this article, we will provide a Q&A guide to help you better understand solving and graphing inequalities.

Q: What is an inequality?

A: An inequality is a mathematical expression that compares two values using greater than, less than, greater than or equal to, or less than or equal to.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality. You can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides of the inequality by the same non-zero value.

Q: What is the difference between a closed and open inequality?

A: A closed inequality is an inequality that includes the endpoint, while an open inequality is an inequality that does not include the endpoint.

Q: How do I graph an inequality?

A: To graph an inequality, you need to plot the endpoints on a number line. If the inequality is closed, you need to include the endpoint in the graph. If the inequality is open, you need to exclude the endpoint from the graph.

Q: What is the purpose of graphing an inequality?

A: The purpose of graphing an inequality is to visualize the solution set of the inequality. This can help you understand the relationship between the variable and the constant in the inequality.

Q: How do I select an endpoint to change it from closed to open?

A: To select an endpoint to change it from closed to open, you need to identify the endpoint that you want to change. Then, you need to change the endpoint from a closed circle to an open circle.

Q: How do I delete a segment, ray, or line?

A: To delete a segment, ray, or line, you need to select the middle of the segment, ray, or line and delete it.

Q: What are some common mistakes to avoid when solving and graphing inequalities?

A: Some common mistakes to avoid when solving and graphing inequalities include:

• Failing to isolate the variable on one side of the inequality.
• Failing to plot the endpoints on a number line.
• Failing to change an endpoint from closed to open when changing an inequality from closed to open.
• Failing to delete a segment, ray, or line by selecting the middle of the segment, ray, or line and deleting it.

Q: What are some real-world applications of solving and graphing inequalities?

A: Some real-world applications of solving and graphing inequalities include:

• Finance: In finance, inequalities are used to model financial transactions and investments.
• Science: In science, inequalities are used to model physical phenomena and predict outcomes.
• Engineering: In engineering, inequalities are used to design and optimize systems.
• Computer Science: In computer science, inequalities are used to model algorithms and data structures.

Conclusion

Solving and graphing inequalities is an essential skill in mathematics, and it requires a clear understanding of the concepts and techniques involved. In this article, we provided a Q&A guide to help you better understand solving and graphing inequalities. We hope that this guide has been helpful in answering your questions and providing you with a better understanding of solving and graphing inequalities.

Additional Resources

• Khan Academy: Inequalities
• Mathway: Inequalities
• Wolfram Alpha: Inequalities

Practice Problems

• Solve the inequality $-5 \leq 2x-3 \ \textless \ 7$.
• Graph the inequality $-3 \leq x \ \textless \ 5$.
• Solve the inequality $-2 \leq \frac{x+1}{2} \ \textless \ 4$.

Answer Key

• $-2 \leq x \ \textless \ 5$
• $-3 \leq x \ \textless \ 5$
• $-9 \leq x \ \textless \ 7$