Evaluate $6h + 30$ When $h = 6$.A. 36 B. 66 C. 96 D. 60

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Understanding the Problem

To evaluate the expression $6h + 30$ when $h = 6$, we need to substitute the value of $h$ into the expression and then simplify it. This involves basic algebraic operations such as multiplication and addition.

Substituting the Value of $h$

The given expression is $6h + 30$, and we are told that $h = 6$. To substitute the value of $h$, we replace $h$ with $6$ in the expression. This gives us:

$$6(6) + 30$$

Simplifying the Expression

Now that we have substituted the value of $h$, we can simplify the expression by performing the multiplication and addition operations.

$$6(6) + 30 = 36 + 30$$

Evaluating the Expression

To evaluate the expression, we need to add $36$ and $30$. This involves basic addition operation.

$$36 + 30 = 66$$

Conclusion

Therefore, the value of the expression $6h + 30$ when $h = 6$ is $66$.

Answer Choice

The correct answer is B. 66.

Why is this Important?

Evaluating expressions with variables is an essential skill in mathematics, particularly in algebra. It helps us to solve equations and inequalities, and to model real-world problems. In this case, we used the substitution method to evaluate the expression $6h + 30$ when $h = 6$. This is a fundamental concept in algebra that has numerous applications in various fields, including science, engineering, and economics.

Real-World Applications

Evaluating expressions with variables has many real-world applications. For example, in business, we may need to evaluate an expression that represents the total cost of producing a certain number of products. In science, we may need to evaluate an expression that represents the distance traveled by an object under the influence of gravity. In engineering, we may need to evaluate an expression that represents the stress on a material under different loads.

Tips and Tricks

When evaluating expressions with variables, it's essential to follow the order of operations (PEMDAS):

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

By following this order of operations, we can ensure that we evaluate expressions correctly and avoid any errors.

Common Mistakes

When evaluating expressions with variables, some common mistakes include:

• Forgetting to substitute the value of the variable.
• Not following the order of operations.
• Making errors in multiplication and division operations.
• Not simplifying the expression correctly.

To avoid these mistakes, it's essential to be careful and methodical when evaluating expressions with variables.

Conclusion

Evaluating expressions with variables is a fundamental concept in mathematics that has numerous applications in various fields. By following the substitution method and the order of operations, we can ensure that we evaluate expressions correctly and avoid any errors. In this article, we evaluated the expression $6h + 30$ when $h = 6$ and found that the correct answer is B. 66.

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Frequently Asked Questions

Q: What is the value of $h$ in the expression $6h + 30$?

A: The value of $h$ is given as $6$.

Q: How do I substitute the value of $h$ into the expression $6h + 30$?

A: To substitute the value of $h$, replace $h$ with $6$ in the expression. This gives us $6(6) + 30$.

Q: What is the next step after substituting the value of $h$?

A: After substituting the value of $h$, we need to simplify the expression by performing the multiplication and addition operations.

Q: How do I simplify the expression $6(6) + 30$?

A: To simplify the expression, we need to perform the multiplication operation first. This gives us $36 + 30$.

Q: What is the final step in evaluating the expression $6h + 30$ when $h = 6$?

A: The final step is to add $36$ and $30$ to get the final value of the expression.

Q: What is the value of the expression $6h + 30$ when $h = 6$?

A: The value of the expression $6h + 30$ when $h = 6$ is $66$.

Q: Why is it essential to follow the order of operations when evaluating expressions with variables?

A: It's essential to follow the order of operations (PEMDAS) to ensure that we evaluate expressions correctly and avoid any errors.

Q: What are some common mistakes to avoid when evaluating expressions with variables?

A: Some common mistakes to avoid include forgetting to substitute the value of the variable, not following the order of operations, making errors in multiplication and division operations, and not simplifying the expression correctly.

Q: How can I ensure that I evaluate expressions with variables correctly?

A: To ensure that you evaluate expressions with variables correctly, be careful and methodical when substituting the value of the variable and following the order of operations.

Q: What are some real-world applications of evaluating expressions with variables?

A: Evaluating expressions with variables has many real-world applications, including business, science, and engineering.

Q: Why is it essential to understand how to evaluate expressions with variables?

A: It's essential to understand how to evaluate expressions with variables because it's a fundamental concept in mathematics that has numerous applications in various fields.

Q: Can you provide an example of a real-world application of evaluating expressions with variables?

A: Yes, in business, we may need to evaluate an expression that represents the total cost of producing a certain number of products. For example, if the cost of producing $x$ units is $6x + 30$, we can evaluate this expression when $x = 6$ to get the total cost.

Q: How can I practice evaluating expressions with variables?

A: You can practice evaluating expressions with variables by working through examples and exercises in your math textbook or online resources.

Q: What are some online resources that can help me practice evaluating expressions with variables?

A: Some online resources that can help you practice evaluating expressions with variables include Khan Academy, Mathway, and Wolfram Alpha.

Q: Can you provide a summary of the key concepts in this article?

A: The key concepts in this article include:

• Substituting the value of the variable into the expression
• Following the order of operations (PEMDAS)
• Simplifying the expression by performing multiplication and addition operations
• Evaluating the expression to get the final value
• Understanding the importance of evaluating expressions with variables in real-world applications

Q: What is the final answer to the problem?

A: The final answer to the problem is B. 66.