Look At The Inequality.$6y \ \textgreater \ 48$Which Set Of Values For $y$ Will Make This Inequality True?A. $4, 5, 6$ B. $6, 8, 11$ C. $8, 9, 12$ D. $9, 11, 12$

Introduction

Inequalities are mathematical expressions that compare two values, indicating whether one is greater than, less than, or equal to the other. In this article, we will focus on solving linear inequalities, specifically the inequality $6y > 48$. We will explore the concept of inequalities, learn how to solve them, and apply this knowledge to find the set of values for $y$ that will make this inequality true.

Understanding Inequalities

An inequality is a mathematical statement that compares two values using the following symbols:

• Greater than ($>$)
• Less than ($<$)
• Greater than or equal to ($\geq$)
• Less than or equal to ($\leq$)

In the given inequality, $6y > 48$, we are comparing the product of $6$ and $y$ to $48$. The inequality states that the product of $6$ and $y$ is greater than $48$.

Solving Linear Inequalities

To solve a linear inequality, we need to isolate the variable on one side of the inequality sign. In this case, we want to isolate $y$. We can do this by dividing both sides of the inequality by $6$.

6y > 48
y > 48/6
y > 8

Finding the Set of Values for $y$

Now that we have solved the inequality, we need to find the set of values for $y$ that will make this inequality true. We can do this by selecting values of $y$ that are greater than $8$.

Let's examine the answer choices:

A. $4, 5, 6$ B. $6, 8, 11$ C. $8, 9, 12$ D. $9, 11, 12$

We can see that only one of these answer choices contains values that are greater than $8$.

Conclusion

In this article, we learned how to solve linear inequalities and applied this knowledge to find the set of values for $y$ that will make the inequality $6y > 48$ true. We discovered that the correct answer is the set of values that contains numbers greater than $8$. This demonstrates the importance of understanding and solving inequalities in mathematics.

Answer

The correct answer is:

C. $8, 9, 12$

Additional Tips and Resources

• To solve a linear inequality, isolate the variable on one side of the inequality sign.
• Use inverse operations to isolate the variable.
• Check your answer by plugging in values from the solution set into the original inequality.
• Practice solving linear inequalities to become more confident and proficient.

Recommended Reading

• Khan Academy: Solving Linear Inequalities
• Mathway: Solving Linear Inequalities
• IXL: Solving Linear Inequalities

Final Thoughts

Q: What is an inequality?

A: An inequality is a mathematical statement that compares two values using the following symbols:

• Greater than ($>$)
• Less than ($<$)
• Greater than or equal to ($\geq$)
• Less than or equal to ($\leq$)

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable on one side of the inequality sign. You can do this by using inverse operations, such as addition, subtraction, multiplication, or division.

Q: What is the first step in solving a linear inequality?

A: The first step in solving a linear inequality is to isolate the variable on one side of the inequality sign. This can be done by adding or subtracting the same value to both sides of the inequality.

Q: How do I know which operation to use when solving a linear inequality?

A: When solving a linear inequality, you need to use the opposite operation of the one that is being performed on the variable. For example, if the inequality is $x + 3 > 5$, you would subtract 3 from both sides to isolate the variable.

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality that can be written in the form $ax + b > c$, where $a$, $b$, and $c$ are constants. A quadratic inequality, on the other hand, is an inequality that can be written in the form $ax^2 + bx + c > 0$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you need to factor the quadratic expression and then use the sign of the expression to determine the solution set.

Q: What is the solution set of an inequality?

A: The solution set of an inequality is the set of all values that make the inequality true. It can be written in interval notation, such as $(a, b)$ or $[a, b]$.

Q: How do I check my answer when solving an inequality?

A: To check your answer when solving an inequality, you need to plug in values from the solution set into the original inequality and verify that the inequality is true.

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

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

• Not isolating the variable on one side of the inequality sign
• Not using the opposite operation when solving the inequality
• Not checking the solution set for extraneous solutions

Q: How can I practice solving inequalities?

A: You can practice solving inequalities by working through examples and exercises in a textbook or online resource. You can also try solving inequalities on your own and then checking your answers with a calculator or online tool.

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

A: Solving inequalities has many real-world applications, including:

• Modeling population growth and decline
• Determining the maximum or minimum value of a function
• Finding the solution to a system of linear equations
• Optimizing a business or financial decision

Conclusion

Solving inequalities is an essential skill in mathematics, and it requires practice and patience to become proficient. By following the steps outlined in this article, you can learn how to solve linear and quadratic inequalities and apply this knowledge to a variety of mathematical problems. Remember to always check your answer and practice solving inequalities to become more confident and proficient.