Solve The Inequality: { \frac{1}{2} X \ \textgreater \ 7$}$Enter The Correct Answer.

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Introduction

In mathematics, inequalities are a fundamental concept that deals with the comparison of two or more expressions. They are used to represent the relationship between variables and constants, and are essential in solving problems in various fields such as algebra, geometry, and calculus. In this article, we will focus on solving the inequality $\frac{1}{2} x \ \textgreater \ 7$, which involves isolating the variable $x$ and determining the range of values that satisfy the given inequality.

Understanding the Inequality

The given inequality is $\frac{1}{2} x \ \textgreater \ 7$. To solve this inequality, we need to isolate the variable $x$ by performing algebraic operations on both sides of the inequality. The goal is to get $x$ by itself on one side of the inequality sign.

Step 1: Multiply Both Sides by 2

To isolate $x$, we can start by multiplying both sides of the inequality by 2. This will eliminate the fraction and make it easier to work with. When we multiply both sides by 2, we get:

$$\frac{1}{2} x \ \textgreater \ 7$$

$$2 \times \frac{1}{2} x \ \textgreater \ 2 \times 7$$

$$x \ \textgreater \ 14$$

Step 2: Analyze the Inequality

Now that we have isolated $x$, we can analyze the inequality to determine the range of values that satisfy it. The inequality $x \ \textgreater \ 14$ indicates that $x$ is greater than 14. This means that any value of $x$ that is greater than 14 will satisfy the inequality.

Step 3: Express the Solution in Interval Notation

To express the solution in interval notation, we can use the following notation:

$$x \ \textgreater \ 14$$

$$x \in (14, \infty)$$

This notation indicates that $x$ is an element of the set of all real numbers greater than 14.

Conclusion

In conclusion, the solution to the inequality $\frac{1}{2} x \ \textgreater \ 7$ is $x \ \textgreater \ 14$. This means that any value of $x$ that is greater than 14 will satisfy the inequality. We can express the solution in interval notation as $x \in (14, \infty)$.

Frequently Asked Questions

• What is the solution to the inequality $\frac{1}{2} x \ \textgreater \ 7$?
• How do we isolate the variable $x$ in the inequality $\frac{1}{2} x \ \textgreater \ 7$?
• What is the range of values that satisfy the inequality $x \ \textgreater \ 14$?

Final Answer

The final answer is $\boxed{x \ \textgreater \ 14}$.

Additional Resources

• For more information on solving inequalities, please refer to the following resources:

• Khan Academy: Solving Inequalities
• Mathway: Solving Inequalities
• Wolfram Alpha: Solving Inequalities

Related Topics

• Solving Linear Inequalities
• Solving Quadratic Inequalities
• Solving Polynomial Inequalities

References

• [1] Khan Academy. (n.d.). Solving Inequalities. Retrieved from https://www.khanacademy.org/math/algebra/x2-2-inequalities/x2-2-1-solve-inequalities/v/solving-inequalities
• [2] Mathway. (n.d.). Solving Inequalities. Retrieved from https://www.mathway.com/subjects/inequalities
• [3] Wolfram Alpha. (n.d.). Solving Inequalities. Retrieved from https://www.wolframalpha.com/input/?i=solving+inequalities
  

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Introduction

In our previous article, we solved the inequality $\frac{1}{2} x \ \textgreater \ 7$ and found that the solution is $x \ \textgreater \ 14$. In this article, we will provide a Q&A section to address some of the common questions and concerns that readers may have.

Q&A

Q: What is the solution to the inequality $\frac{1}{2} x \ \textgreater \ 7$?

A: The solution to the inequality $\frac{1}{2} x \ \textgreater \ 7$ is $x \ \textgreater \ 14$. This means that any value of $x$ that is greater than 14 will satisfy the inequality.

Q: How do we isolate the variable $x$ in the inequality $\frac{1}{2} x \ \textgreater \ 7$?

A: To isolate the variable $x$, we can start by multiplying both sides of the inequality by 2. This will eliminate the fraction and make it easier to work with. When we multiply both sides by 2, we get:

$$\frac{1}{2} x \ \textgreater \ 7$$

$$2 \times \frac{1}{2} x \ \textgreater \ 2 \times 7$$

$$x \ \textgreater \ 14$$

Q: What is the range of values that satisfy the inequality $x \ \textgreater \ 14$?

A: The range of values that satisfy the inequality $x \ \textgreater \ 14$ is all real numbers greater than 14. This can be expressed in interval notation as $x \in (14, \infty)$.

Q: Can I use a calculator to solve the inequality $\frac{1}{2} x \ \textgreater \ 7$?

A: Yes, you can use a calculator to solve the inequality $\frac{1}{2} x \ \textgreater \ 7$. However, it's always a good idea to check your work by hand to make sure you understand the solution.

Q: How do I graph the solution to the inequality $\frac{1}{2} x \ \textgreater \ 7$?

A: To graph the solution to the inequality $\frac{1}{2} x \ \textgreater \ 7$, you can use a number line or a graphing calculator. The solution is all real numbers greater than 14, so you can shade the region to the right of 14 on the number line.

Q: Can I use the same method to solve other inequalities?

A: Yes, you can use the same method to solve other inequalities. The key is to isolate the variable and determine the range of values that satisfy the inequality.

Conclusion

In conclusion, solving the inequality $\frac{1}{2} x \ \textgreater \ 7$ requires isolating the variable $x$ and determining the range of values that satisfy the inequality. We hope this Q&A section has helped to clarify any questions or concerns you may have had.

Frequently Asked Questions

• What is the solution to the inequality $\frac{1}{2} x \ \textgreater \ 7$?
• How do we isolate the variable $x$ in the inequality $\frac{1}{2} x \ \textgreater \ 7$?
• What is the range of values that satisfy the inequality $x \ \textgreater \ 14$?
• Can I use a calculator to solve the inequality $\frac{1}{2} x \ \textgreater \ 7$?
• How do I graph the solution to the inequality $\frac{1}{2} x \ \textgreater \ 7$?

Final Answer

The final answer is $\boxed{x \ \textgreater \ 14}$.

Additional Resources

• For more information on solving inequalities, please refer to the following resources:

• Khan Academy: Solving Inequalities
• Mathway: Solving Inequalities
• Wolfram Alpha: Solving Inequalities

Related Topics

• Solving Linear Inequalities
• Solving Quadratic Inequalities
• Solving Polynomial Inequalities

References

• [1] Khan Academy. (n.d.). Solving Inequalities. Retrieved from https://www.khanacademy.org/math/algebra/x2-2-inequalities/x2-2-1-solve-inequalities/v/solving-inequalities
• [2] Mathway. (n.d.). Solving Inequalities. Retrieved from https://www.mathway.com/subjects/inequalities
• [3] Wolfram Alpha. (n.d.). Solving Inequalities. Retrieved from https://www.wolframalpha.com/input/?i=solving+inequalities