Six Times A Number Is Greater Than 20 More Than That Number. What Are The Possible Values Of That Number?A. \[$n \ \textless \ 4\$\] B. \[$n \ \textgreater \ 4\$\] C. \[$n \ \textgreater \ \frac{20}{7}\$\] D. \[$n \
Introduction
In this article, we will explore the possible values of a number that satisfies the condition: six times the number is greater than 20 more than that number. This problem can be represented mathematically as 6n > n + 20, where n is the unknown number. We will analyze this inequality and determine the possible values of n that satisfy the given condition.
Understanding the Inequality
To begin with, let's understand the given inequality 6n > n + 20. This inequality states that six times the number n is greater than the number n plus 20. We can simplify this inequality by subtracting n from both sides, which gives us 5n > 20.
Solving the Inequality
Now, let's solve the inequality 5n > 20. To do this, we can divide both sides of the inequality by 5, which gives us n > 4. This means that the number n must be greater than 4 to satisfy the given condition.
Analyzing the Possible Values of n
Based on the inequality n > 4, we can conclude that the possible values of n are all real numbers greater than 4. This can be represented mathematically as n ∈ (4, ∞). In other words, n can take any value greater than 4, and the inequality will still hold true.
Comparing with the Given Options
Now, let's compare our result with the given options:
A. n < 4 B. n > 4 C. n > 20/7 D. n > 4
Based on our analysis, we can see that option B is the correct answer. The possible values of n are indeed all real numbers greater than 4.
Conclusion
In conclusion, we have analyzed the inequality 6n > n + 20 and determined the possible values of the number n that satisfy the given condition. We found that n must be greater than 4, and the possible values of n are all real numbers greater than 4. This can be represented mathematically as n ∈ (4, ∞). We compared our result with the given options and found that option B is the correct answer.
Frequently Asked Questions
Q: What is the inequality 6n > n + 20?
A: The inequality 6n > n + 20 states that six times the number n is greater than the number n plus 20.
Q: How do we solve the inequality 5n > 20?
A: We can solve the inequality 5n > 20 by dividing both sides of the inequality by 5, which gives us n > 4.
Q: What are the possible values of n that satisfy the given condition?
A: The possible values of n are all real numbers greater than 4, which can be represented mathematically as n ∈ (4, ∞).
Q: Which option is the correct answer?
A: Option B is the correct answer, which states that n > 4.
Final Answer
The final answer is option B: n > 4.
Introduction
In our previous article, we explored the possible values of a number that satisfies the condition: six times the number is greater than 20 more than that number. We analyzed the inequality 6n > n + 20 and determined that the possible values of n are all real numbers greater than 4. In this article, we will provide a Q&A section to further clarify any doubts and provide additional information on the topic.
Q&A
Q: What is the main condition that we are trying to satisfy in this problem?
A: The main condition is that six times the number n is greater than 20 more than that number, which can be represented mathematically as 6n > n + 20.
Q: How do we simplify the inequality 6n > n + 20?
A: We can simplify the inequality 6n > n + 20 by subtracting n from both sides, which gives us 5n > 20.
Q: How do we solve the inequality 5n > 20?
A: We can solve the inequality 5n > 20 by dividing both sides of the inequality by 5, which gives us n > 4.
Q: What are the possible values of n that satisfy the given condition?
A: The possible values of n are all real numbers greater than 4, which can be represented mathematically as n ∈ (4, ∞).
Q: Why is option A (n < 4) incorrect?
A: Option A (n < 4) is incorrect because it states that n is less than 4, which contradicts the fact that n must be greater than 4 to satisfy the given condition.
Q: Why is option C (n > 20/7) incorrect?
A: Option C (n > 20/7) is incorrect because it states that n is greater than 20/7, which is not the correct condition. The correct condition is that n must be greater than 4.
Q: What is the significance of the inequality 6n > n + 20 in real-life scenarios?
A: The inequality 6n > n + 20 can be used to model real-life scenarios where a quantity is increasing at a certain rate. For example, if a company's sales are increasing at a rate of 6% per year, and the current sales are $100,000, then the inequality 6n > n + 20 can be used to determine the minimum sales required to achieve a certain profit margin.
Q: How can we use the inequality 6n > n + 20 to make decisions in business or finance?
A: The inequality 6n > n + 20 can be used to make decisions in business or finance by determining the minimum investment or sales required to achieve a certain return on investment. For example, if a company is considering investing in a new project, the inequality 6n > n + 20 can be used to determine the minimum investment required to achieve a certain return on investment.
Conclusion
In conclusion, we have provided a Q&A section to further clarify any doubts and provide additional information on the topic of the inequality 6n > n + 20. We hope that this Q&A section has been helpful in understanding the concept and its applications in real-life scenarios.
Frequently Asked Questions
Q: What is the main condition that we are trying to satisfy in this problem?
A: The main condition is that six times the number n is greater than 20 more than that number, which can be represented mathematically as 6n > n + 20.
Q: How do we simplify the inequality 6n > n + 20?
A: We can simplify the inequality 6n > n + 20 by subtracting n from both sides, which gives us 5n > 20.
Q: How do we solve the inequality 5n > 20?
A: We can solve the inequality 5n > 20 by dividing both sides of the inequality by 5, which gives us n > 4.
Q: What are the possible values of n that satisfy the given condition?
A: The possible values of n are all real numbers greater than 4, which can be represented mathematically as n ∈ (4, ∞).
Final Answer
The final answer is option B: n > 4.