Ten Less Than Twice A Number Is Equal To At Most 52. What Are All The Possible Values Of The Number?Inuk Wrote The Inequality $2x - 10 \leq 52$, Where $x$ Equals The Number, To Help Solve This Problem. Solve His Inequality. Use The

Introduction

In mathematics, inequalities are used to represent relationships between variables that are not equal. In this article, we will focus on solving an inequality that represents a real-world problem. The problem states that ten less than twice a number is equal to at most 52. We will use the given inequality $2x - 10 \leq 52$ to solve for the possible values of the number.

Understanding the Inequality

The given inequality is $2x - 10 \leq 52$. To solve this inequality, we need to isolate the variable $x$. The first step is to add 10 to both sides of the inequality, which will eliminate the negative term.

Adding 10 to Both Sides

2x - 10 + 10 \leq 52 + 10

This simplifies to:

2x \leq 62

Isolating the Variable

Now that we have isolated the term with the variable, we can solve for $x$. To do this, we need to divide both sides of the inequality by 2.

Dividing Both Sides by 2

\frac{2x}{2} \leq \frac{62}{2}

This simplifies to:

x \leq 31

Conclusion

The inequality $2x - 10 \leq 52$ represents the relationship between the number $x$ and the value 52. By solving the inequality, we have found that the possible values of the number $x$ are all values less than or equal to 31.

Possible Values of the Number

The possible values of the number $x$ are all values less than or equal to 31. This means that the number $x$ can be any value from negative infinity to 31, inclusive.

Example Values

Some example values of the number $x$ include:

• $x = 0$
• $x = 10$
• $x = 20$
• $x = 30$
• $x = 31$

Graphical Representation

The inequality $x \leq 31$ can be represented graphically on a number line. The number line is divided into two parts: the part to the left of 31 and the part to the right of 31. The inequality states that the number $x$ is less than or equal to 31, so the solution set is the part of the number line to the left of 31.

Graphical Representation

  -∞ | 31 | ∞
  ---|----|---
  x  | ≤  | 

Real-World Applications

The inequality $2x - 10 \leq 52$ has many real-world applications. For example, in business, the inequality can be used to represent the maximum amount of profit that a company can make. In finance, the inequality can be used to represent the maximum amount of money that a person can borrow.

Real-World Applications

Some real-world applications of the inequality $2x - 10 \leq 52$ include:

• Business: The inequality can be used to represent the maximum amount of profit that a company can make.
• Finance: The inequality can be used to represent the maximum amount of money that a person can borrow.
• Science: The inequality can be used to represent the maximum amount of a substance that can be produced.

Conclusion

In conclusion, the inequality $2x - 10 \leq 52$ represents the relationship between the number $x$ and the value 52. By solving the inequality, we have found that the possible values of the number $x$ are all values less than or equal to 31. The inequality has many real-world applications, including business, finance, and science.

Final Answer

The final answer is $\boxed{31}$.

Introduction

In our previous article, we solved the inequality $2x - 10 \leq 52$ to find the possible values of the number $x$. In this article, we will answer some common questions related to the inequality and its solution.

Q&A

Q: What is the inequality $2x - 10 \leq 52$ trying to represent?

A: The inequality $2x - 10 \leq 52$ is trying to represent the relationship between the number $x$ and the value 52. Specifically, it is saying that ten less than twice a number is equal to at most 52.

Q: How do I solve the inequality $2x - 10 \leq 52$?

A: To solve the inequality $2x - 10 \leq 52$, you need to isolate the variable $x$. First, add 10 to both sides of the inequality to get $2x \leq 62$. Then, divide both sides of the inequality by 2 to get $x \leq 31$.

Q: What are the possible values of the number $x$?

A: The possible values of the number $x$ are all values less than or equal to 31. This means that the number $x$ can be any value from negative infinity to 31, inclusive.

Q: Can I use the inequality $2x - 10 \leq 52$ to represent a real-world problem?

A: Yes, the inequality $2x - 10 \leq 52$ can be used to represent a real-world problem. For example, in business, the inequality can be used to represent the maximum amount of profit that a company can make. In finance, the inequality can be used to represent the maximum amount of money that a person can borrow.

Q: How do I graph the inequality $x \leq 31$ on a number line?

A: To graph the inequality $x \leq 31$ on a number line, you need to divide the number line into two parts: the part to the left of 31 and the part to the right of 31. The inequality states that the number $x$ is less than or equal to 31, so the solution set is the part of the number line to the left of 31.

Q: What are some real-world applications of the inequality $2x - 10 \leq 52$?

A: Some real-world applications of the inequality $2x - 10 \leq 52$ include:

• Business: The inequality can be used to represent the maximum amount of profit that a company can make.
• Finance: The inequality can be used to represent the maximum amount of money that a person can borrow.
• Science: The inequality can be used to represent the maximum amount of a substance that can be produced.

Conclusion

In conclusion, the inequality $2x - 10 \leq 52$ represents the relationship between the number $x$ and the value 52. By solving the inequality, we have found that the possible values of the number $x$ are all values less than or equal to 31. The inequality has many real-world applications, including business, finance, and science.

Final Answer

The final answer is $\boxed{31}$.

Additional Resources

If you have any additional questions or need further clarification on the inequality $2x - 10 \leq 52$, please refer to the following resources:

• Mathematics textbooks: You can find the solution to the inequality $2x - 10 \leq 52$ in most mathematics textbooks.
• Online resources: You can find online resources, such as Khan Academy and Mathway, that provide step-by-step solutions to the inequality $2x - 10 \leq 52$.
• Mathematical software: You can use mathematical software, such as Mathematica and Maple, to solve the inequality $2x - 10 \leq 52$.