What Inequality Describes The Solutions Of $2y \leq 8$?$y \leq \square$

Introduction

In mathematics, inequalities are used to describe the relationship between two or more values. They are an essential part of algebra and are used to solve equations, find the maximum or minimum value of a function, and determine the range of values that satisfy a given condition. In this article, we will explore the inequality that describes the solutions of the equation $2y \leq 8$.

Understanding the Equation

The equation $2y \leq 8$ is a linear inequality, which means that it can be written in the form $ax \leq b$, where $a$ and $b$ are constants. In this case, the equation can be rewritten as $y \leq 4$. This means that the value of $y$ must be less than or equal to 4.

Solving the Inequality

To solve the inequality $2y \leq 8$, we need to isolate the variable $y$. We can do this by dividing both sides of the inequality by 2. This gives us:

$$\frac{2y}{2} \leq \frac{8}{2}$$

Simplifying the inequality, we get:

$$y \leq 4$$

Graphing the Solution

The solution to the inequality $y \leq 4$ can be graphed on a number line. The number line is a line that extends infinitely in both directions, with numbers marked at regular intervals. To graph the solution, we need to shade the region to the left of the number 4.

Writing the Inequality in Interval Notation

The solution to the inequality $y \leq 4$ can also be written in interval notation. Interval notation is a way of writing a set of numbers using square brackets and parentheses. In this case, the solution can be written as:

$$(-\infty, 4]$$

This means that the value of $y$ can be any real number less than or equal to 4.

Conclusion

In conclusion, the inequality that describes the solutions of the equation $2y \leq 8$ is $y \leq 4$. This means that the value of $y$ must be less than or equal to 4. The solution can be graphed on a number line and written in interval notation as $(-\infty, 4]$.

Frequently Asked Questions

• What is the solution to the inequality $2y \leq 8$?
• How do you graph the solution to the inequality $y \leq 4$?
• What is the interval notation for the solution to the inequality $y \leq 4$?

Final Answer

The final answer is $y \leq 4$.

Introduction

In the previous article, we explored the inequality that describes the solutions of the equation $2y \leq 8$. In this article, we will answer some of the most frequently asked questions related to this topic.

Q&A

Q: What is the solution to the inequality $2y \leq 8$?

A: The solution to the inequality $2y \leq 8$ is $y \leq 4$. This means that the value of $y$ must be less than or equal to 4.

Q: How do you graph the solution to the inequality $y \leq 4$?

A: To graph the solution to the inequality $y \leq 4$, you need to shade the region to the left of the number 4 on a number line. This represents all the values of $y$ that are less than or equal to 4.

Q: What is the interval notation for the solution to the inequality $y \leq 4$?

A: The interval notation for the solution to the inequality $y \leq 4$ is $(-\infty, 4]$. This means that the value of $y$ can be any real number less than or equal to 4.

Q: How do you solve the inequality $2y \leq 8$?

A: To solve the inequality $2y \leq 8$, you need to isolate the variable $y$ by dividing both sides of the inequality by 2. This gives you:

$$\frac{2y}{2} \leq \frac{8}{2}$$

Simplifying the inequality, you get:

$$y \leq 4$$

Q: What is the difference between the inequality $y \leq 4$ and the equation $y = 4$?

A: The inequality $y \leq 4$ represents all the values of $y$ that are less than or equal to 4, including 4 itself. The equation $y = 4$, on the other hand, represents only the value of $y$ that is equal to 4.

Q: Can you give an example of a value of $y$ that satisfies the inequality $y \leq 4$?

A: Yes, an example of a value of $y$ that satisfies the inequality $y \leq 4$ is $y = 3$. This is because 3 is less than 4, so it satisfies the inequality.

Q: Can you give an example of a value of $y$ that does not satisfy the inequality $y \leq 4$?

A: Yes, an example of a value of $y$ that does not satisfy the inequality $y \leq 4$ is $y = 5$. This is because 5 is greater than 4, so it does not satisfy the inequality.

Conclusion

In conclusion, we have answered some of the most frequently asked questions related to the inequality that describes the solutions of the equation $2y \leq 8$. We hope that this article has been helpful in clarifying any confusion and providing a better understanding of this topic.

Final Answer

The final answer is $y \leq 4$.