What Is The Value Of The Expression two Less Than Six Times The Difference Of A Number And Five When N = 9 N = 9 N = 9 ?A. 22 B. 16 C. 32 D. 31

Understanding the Problem

The problem requires us to find the value of a given expression when a specific number is substituted for the variable $n$. The expression is "two less than six times the difference of a number and five," which can be translated into a mathematical equation as $6(n - 5) - 2$. We are given that $n = 9$, and we need to find the value of the expression when this value is substituted for $n$.

Breaking Down the Expression

To solve this problem, we need to break down the expression into simpler components and then substitute the given value of $n$ into the expression. The expression can be broken down as follows:

• The difference of a number and five is $n - 5$.
• Six times the difference is $6(n - 5)$.
• Two less than six times the difference is $6(n - 5) - 2$.

Substituting the Value of $n$

Now that we have broken down the expression, we can substitute the given value of $n$ into the expression. We are given that $n = 9$, so we can substitute this value into the expression as follows:

$$6(9 - 5) - 2$$

Evaluating the Expression

To find the value of the expression, we need to evaluate the expression by following the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses: $9 - 5 = 4$
2. Multiply 6 by the result: $6 \times 4 = 24$
3. Subtract 2 from the result: $24 - 2 = 22$

Conclusion

Therefore, the value of the expression "two less than six times the difference of a number and five" when $n = 9$ is 22.

Step-by-Step Solution

Here is the step-by-step solution to the problem:

1. Break down the expression into simpler components:
   • The difference of a number and five is $n - 5$.
   • Six times the difference is $6(n - 5)$.
   • Two less than six times the difference is $6(n - 5) - 2$.
2. Substitute the given value of $n$ into the expression: $6(9 - 5) - 2$
3. Evaluate the expression inside the parentheses: $9 - 5 = 4$
4. Multiply 6 by the result: $6 \times 4 = 24$
5. Subtract 2 from the result: $24 - 2 = 22$

Final Answer

The final answer is $\boxed{22}$.

Frequently Asked Questions

Q: What is the value of the expression "two less than six times the difference of a number and five" when $n = 9$?

A: The value of the expression is 22.

Q: How do I break down the expression into simpler components?

A: To break down the expression, you need to follow these steps:

• The difference of a number and five is $n - 5$.
• Six times the difference is $6(n - 5)$.
• Two less than six times the difference is $6(n - 5) - 2$.

Q: How do I substitute the value of $n$ into the expression?

A: To substitute the value of $n$ into the expression, you need to replace $n$ with the given value. For example, if $n = 9$, you would substitute 9 into the expression as follows:

$$6(9 - 5) - 2$$

Q: What is the order of operations (PEMDAS) and how do I use it to evaluate the expression?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate any multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

To use PEMDAS to evaluate the expression, you would follow these steps:

1. Evaluate the expression inside the parentheses: $9 - 5 = 4$
2. Multiply 6 by the result: $6 \times 4 = 24$
3. Subtract 2 from the result: $24 - 2 = 22$

Q: What is the final answer to the problem?

A: The final answer to the problem is 22.

Additional Resources

If you are having trouble understanding the problem or need additional help, here are some additional resources that may be helpful:

• Mathematics Tutorial: This website provides a comprehensive tutorial on mathematics, including algebra and expressions.
• Expression Evaluator: This website provides an expression evaluator that can help you evaluate expressions and check your work.
• Mathematics Forum: This website provides a forum where you can ask questions and get help from other mathematicians.

Conclusion

In conclusion, the value of the expression "two less than six times the difference of a number and five" when $n = 9$ is 22. We hope that this Q&A article has been helpful in understanding the problem and providing additional resources for those who need help.