Sharayah Graphs The Compound Inequality Below. Which Statement About Her Graph Is TRUE?3x + 6 < 12 Or 2x – 8 > 20A. The Endpoint At 2 Is An Open Circle, And The Endpoint At 14 Is A Closed Circle.B. The Arrow Will Go To The Right From 2.C. Both
Introduction
In mathematics, inequalities are used to describe relationships between variables. A compound inequality is a combination of two or more inequalities, connected by logical operators such as "and" or "or." Graphing compound inequalities is an essential skill in algebra, as it helps us visualize the solution set and understand the relationships between the variables. In this article, we will explore the concept of graphing compound inequalities, with a focus on the statement about Sharayah's graph.
Understanding Compound Inequalities
A compound inequality is a statement that combines two or more inequalities using logical operators. For example, the compound inequality 3x + 6 < 12 or 2x – 8 > 20 is a combination of two inequalities: 3x + 6 < 12 and 2x – 8 > 20. The logical operator "or" is used to connect the two inequalities.
Graphing Compound Inequalities
To graph a compound inequality, we need to graph each individual inequality separately and then combine the results. When graphing a compound inequality, we use the following rules:
- For the inequality 3x + 6 < 12, we graph the inequality 3x < 6 by subtracting 6 from both sides, resulting in 3x < 6. We then divide both sides by 3, resulting in x < 2.
- For the inequality 2x – 8 > 20, we graph the inequality 2x > 28 by adding 8 to both sides, resulting in 2x > 28. We then divide both sides by 2, resulting in x > 14.
Graphing the Compound Inequality
To graph the compound inequality 3x + 6 < 12 or 2x – 8 > 20, we need to graph each individual inequality separately and then combine the results. The graph of the compound inequality will consist of two parts: the graph of the inequality 3x + 6 < 12 and the graph of the inequality 2x – 8 > 20.
Analyzing the Graph
Let's analyze the graph of the compound inequality 3x + 6 < 12 or 2x – 8 > 20. The graph consists of two parts: the graph of the inequality 3x + 6 < 12 and the graph of the inequality 2x – 8 > 20.
- The graph of the inequality 3x + 6 < 12 is a line with a slope of 3 and a y-intercept of -6. The line is dashed, indicating that the inequality is strict.
- The graph of the inequality 2x – 8 > 20 is a line with a slope of 2 and a y-intercept of 28. The line is dashed, indicating that the inequality is strict.
Conclusion
In conclusion, the graph of the compound inequality 3x + 6 < 12 or 2x – 8 > 20 consists of two parts: the graph of the inequality 3x + 6 < 12 and the graph of the inequality 2x – 8 > 20. The graph is a combination of two lines, with the line representing the inequality 3x + 6 < 12 being dashed and the line representing the inequality 2x – 8 > 20 being dashed.
Answer to the Question
The correct answer to the question is:
- A. The endpoint at 2 is an open circle, and the endpoint at 14 is a closed circle.
This is because the graph of the compound inequality 3x + 6 < 12 or 2x – 8 > 20 consists of two parts: the graph of the inequality 3x + 6 < 12 and the graph of the inequality 2x – 8 > 20. The endpoint at 2 is an open circle, indicating that the inequality 3x + 6 < 12 is strict. The endpoint at 14 is a closed circle, indicating that the inequality 2x – 8 > 20 is not strict.
Final Thoughts
Q: What is a compound inequality?
A: A compound inequality is a combination of two or more inequalities, connected by logical operators such as "and" or "or." For example, the compound inequality 3x + 6 < 12 or 2x – 8 > 20 is a combination of two inequalities: 3x + 6 < 12 and 2x – 8 > 20.
Q: How do I graph a compound inequality?
A: To graph a compound inequality, you need to graph each individual inequality separately and then combine the results. When graphing a compound inequality, you use the following rules:
- For the inequality 3x + 6 < 12, you graph the inequality 3x < 6 by subtracting 6 from both sides, resulting in 3x < 6. You then divide both sides by 3, resulting in x < 2.
- For the inequality 2x – 8 > 20, you graph the inequality 2x > 28 by adding 8 to both sides, resulting in 2x > 28. You then divide both sides by 2, resulting in x > 14.
Q: What is the difference between a strict inequality and a non-strict inequality?
A: A strict inequality is an inequality that is not equal to. For example, the inequality 3x + 6 < 12 is a strict inequality. A non-strict inequality is an inequality that is equal to. For example, the inequality 3x + 6 ≤ 12 is a non-strict inequality.
Q: How do I determine whether an endpoint is open or closed?
A: To determine whether an endpoint is open or closed, you need to look at the inequality. If the inequality is strict, the endpoint is open. If the inequality is non-strict, the endpoint is closed.
Q: What is the purpose of graphing compound inequalities?
A: The purpose of graphing compound inequalities is to visualize the solution set and understand the relationships between the variables. By graphing compound inequalities, you can see the intersection of the two inequalities and understand how they relate to each other.
Q: Can I use graphing compound inequalities to solve real-world problems?
A: Yes, you can use graphing compound inequalities to solve real-world problems. For example, you can use graphing compound inequalities to model the relationship between two variables in a real-world scenario.
Q: What are some common mistakes to avoid when graphing compound inequalities?
A: Some common mistakes to avoid when graphing compound inequalities include:
- Not graphing each individual inequality separately
- Not combining the results correctly
- Not paying attention to the direction of the inequality
- Not using the correct notation for the inequality
Q: How can I practice graphing compound inequalities?
A: You can practice graphing compound inequalities by working through examples and exercises in your textbook or online resources. You can also try graphing compound inequalities on your own using real-world scenarios or problems.
Q: What are some resources available for learning about graphing compound inequalities?
A: Some resources available for learning about graphing compound inequalities include:
- Textbooks and online resources
- Video tutorials and online courses
- Practice problems and exercises
- Real-world scenarios and applications
Conclusion
Graphing compound inequalities is an essential skill in algebra, as it helps us visualize the solution set and understand the relationships between the variables. By following the rules for graphing compound inequalities, we can create accurate and informative graphs that help us understand the relationships between the variables.