Select The Values That Make The Inequality $z \leq -8$ True.Numbers Written In Order From Least To Greatest:-16, -13, -11, -9, -8.1, -8.01, -8.001, -8

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Introduction

In mathematics, inequalities are used to compare values and determine the relationships between them. One of the most common types of inequalities is the less than or equal to inequality, denoted by $\leq$. In this article, we will explore the concept of the inequality $z \leq -8$ and determine which values make this inequality true.

Understanding the Inequality

The inequality $z \leq -8$ states that the value of $z$ is less than or equal to $-8$. This means that any value of $z$ that is less than or equal to $-8$ will make the inequality true. To determine which values make this inequality true, we need to compare the given values to $-8$.

Given Values

The given values are: -16, -13, -11, -9, -8.1, -8.01, -8.001, and -8. These values are written in order from least to greatest.

Comparing Values

To determine which values make the inequality $z \leq -8$ true, we need to compare each value to $-8$. If a value is less than or equal to $-8$, it will make the inequality true.

Value -16

The value -16 is less than -8. Therefore, -16 makes the inequality $z \leq -8$ true.

Value -13

The value -13 is less than -8. Therefore, -13 makes the inequality $z \leq -8$ true.

Value -11

The value -11 is less than -8. Therefore, -11 makes the inequality $z \leq -8$ true.

Value -9

The value -9 is less than -8. Therefore, -9 makes the inequality $z \leq -8$ true.

Value -8.1

The value -8.1 is less than -8. Therefore, -8.1 makes the inequality $z \leq -8$ true.

Value -8.01

The value -8.01 is less than -8. Therefore, -8.01 makes the inequality $z \leq -8$ true.

Value -8.001

The value -8.001 is less than -8. Therefore, -8.001 makes the inequality $z \leq -8$ true.

Value -8

The value -8 is equal to -8. Therefore, -8 makes the inequality $z \leq -8$ true.

Conclusion

In conclusion, the values that make the inequality $z \leq -8$ true are: -16, -13, -11, -9, -8.1, -8.01, -8.001, and -8. These values are all less than or equal to -8, which makes the inequality true.

Frequently Asked Questions

Q: What is the inequality $z \leq -8$?

A: The inequality $z \leq -8$ states that the value of $z$ is less than or equal to $-8$.

Q: Which values make the inequality $z \leq -8$ true?

A: The values that make the inequality $z \leq -8$ true are: -16, -13, -11, -9, -8.1, -8.01, -8.001, and -8.

Q: How do I determine which values make the inequality $z \leq -8$ true?

A: To determine which values make the inequality $z \leq -8$ true, you need to compare each value to $-8$. If a value is less than or equal to $-8$, it will make the inequality true.

Final Thoughts

In conclusion, the inequality $z \leq -8$ is a simple yet powerful tool for comparing values. By understanding the concept of the inequality and comparing values to $-8$, you can determine which values make the inequality true. Remember, the values that make the inequality $z \leq -8$ true are: -16, -13, -11, -9, -8.1, -8.01, -8.001, and -8.

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Introduction

In our previous article, we explored the concept of the inequality $z \leq -8$ and determined which values make this inequality true. In this article, we will answer some frequently asked questions about the inequality $z \leq -8$.

Q&A

Q: What is the inequality $z \leq -8$?

A: The inequality $z \leq -8$ states that the value of $z$ is less than or equal to $-8$. This means that any value of $z$ that is less than or equal to $-8$ will make the inequality true.

Q: Which values make the inequality $z \leq -8$ true?

A: The values that make the inequality $z \leq -8$ true are: -16, -13, -11, -9, -8.1, -8.01, -8.001, and -8.

Q: How do I determine which values make the inequality $z \leq -8$ true?

A: To determine which values make the inequality $z \leq -8$ true, you need to compare each value to $-8$. If a value is less than or equal to $-8$, it will make the inequality true.

Q: What is the difference between the inequality $z \leq -8$ and the inequality $z < -8$?

A: The inequality $z \leq -8$ includes the value $-8$, while the inequality $z < -8$ does not include the value $-8$. This means that the inequality $z \leq -8$ is true for values that are less than or equal to $-8$, while the inequality $z < -8$ is true for values that are strictly less than $-8$.

Q: Can I use the inequality $z \leq -8$ to compare values that are greater than $-8$?

A: No, the inequality $z \leq -8$ is only used to compare values that are less than or equal to $-8$. If you want to compare values that are greater than $-8$, you will need to use a different inequality.

Q: How do I graph the inequality $z \leq -8$ on a number line?

A: To graph the inequality $z \leq -8$ on a number line, you will need to draw a line at $-8$ and shade the region to the left of the line. This represents all values that are less than or equal to $-8$.

Q: Can I use the inequality $z \leq -8$ to solve equations?

A: Yes, the inequality $z \leq -8$ can be used to solve equations. For example, if you have the equation $z + 2 = -6$, you can use the inequality $z \leq -8$ to determine the solution.

Q: How do I use the inequality $z \leq -8$ to solve systems of equations?

A: To use the inequality $z \leq -8$ to solve systems of equations, you will need to substitute the inequality into one of the equations and solve for the other variable.

Conclusion

In conclusion, the inequality $z \leq -8$ is a powerful tool for comparing values and solving equations. By understanding the concept of the inequality and how to use it, you can solve a wide range of problems.

Final Thoughts

Remember, the inequality $z \leq -8$ is only used to compare values that are less than or equal to $-8$. If you want to compare values that are greater than $-8$, you will need to use a different inequality.