Find The Value Of C C C When D = 6 D = 6 D = 6 . C = 4 D − 7 C = 4d - 7 C = 4 D − 7

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Introduction

In mathematics, equations are used to represent relationships between variables. One of the fundamental concepts in algebra is solving for a variable in an equation. In this article, we will focus on finding the value of $c$ in the equation $c = 4d - 7$, given that $d = 6$. This problem requires us to substitute the value of $d$ into the equation and then solve for $c$.

Understanding the Equation

The equation $c = 4d - 7$ is a linear equation, where $c$ is the dependent variable and $d$ is the independent variable. The equation states that $c$ is equal to four times the value of $d$, minus seven. To find the value of $c$, we need to substitute the value of $d$ into the equation and then simplify.

Substituting the Value of $d$

Given that $d = 6$, we can substitute this value into the equation $c = 4d - 7$. This gives us:

$c = 4(6) - 7$

Simplifying the Equation

To simplify the equation, we need to follow the order of operations (PEMDAS):

1. Multiply 4 and 6: $4(6) = 24$
2. Subtract 7 from 24: $24 - 7 = 17$

Therefore, the value of $c$ is 17.

Conclusion

In this article, we have found the value of $c$ in the equation $c = 4d - 7$, given that $d = 6$. By substituting the value of $d$ into the equation and simplifying, we have determined that the value of $c$ is 17. This problem demonstrates the importance of following the order of operations and simplifying equations to find the solution.

Real-World Applications

The concept of solving for a variable in an equation has numerous real-world applications. In science, technology, engineering, and mathematics (STEM) fields, equations are used to model real-world phenomena and make predictions. For example, in physics, equations are used to describe the motion of objects and predict their trajectories. In economics, equations are used to model the behavior of markets and make predictions about future trends.

Tips and Tricks

When solving for a variable in an equation, it is essential to follow the order of operations (PEMDAS). This ensures that the equation is simplified correctly and the solution is accurate. Additionally, it is crucial to check the units of the variables to ensure that they are consistent. For example, if the equation involves a variable with units of length, the solution should also have units of length.

Common Mistakes

One common mistake when solving for a variable in an equation is to forget to follow the order of operations. This can lead to incorrect solutions and errors in calculations. Another common mistake is to substitute the value of the variable into the equation incorrectly. This can also lead to incorrect solutions and errors in calculations.

Final Thoughts

In conclusion, finding the value of $c$ in the equation $c = 4d - 7$ is a straightforward problem that requires substituting the value of $d$ into the equation and simplifying. However, this problem demonstrates the importance of following the order of operations and simplifying equations to find the solution. By practicing and mastering this concept, students can develop a strong foundation in algebra and apply it to real-world problems.

Additional Resources

For additional resources and practice problems, students can refer to the following:

• Khan Academy: Algebra
• Mathway: Algebra Solver
• Wolfram Alpha: Algebra Calculator

By following these resources and practicing regularly, students can develop a deep understanding of algebra and apply it to real-world problems.

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Introduction

In our previous article, we discussed how to find the value of $c$ in the equation $c = 4d - 7$, given that $d = 6$. In this article, we will address some frequently asked questions (FAQs) related to this topic.

Q&A

Q: What is the equation $c = 4d - 7$?

A: The equation $c = 4d - 7$ is a linear equation, where $c$ is the dependent variable and $d$ is the independent variable. The equation states that $c$ is equal to four times the value of $d$, minus seven.

Q: How do I find the value of $c$ in the equation $c = 4d - 7$?

A: To find the value of $c$, you need to substitute the value of $d$ into the equation and then simplify. For example, if $d = 6$, you would substitute this value into the equation and get $c = 4(6) - 7$.

Q: What is the order of operations (PEMDAS)?

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

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.

Q: Why is it important to follow the order of operations (PEMDAS)?

A: Following the order of operations (PEMDAS) ensures that you simplify expressions correctly and avoid errors. If you don't follow the order of operations, you may get incorrect results.

Q: What is the value of $c$ in the equation $c = 4d - 7$ when $d = 6$?

A: To find the value of $c$, you need to substitute the value of $d$ into the equation and then simplify. Using the equation $c = 4d - 7$ and substituting $d = 6$, you get:

$c = 4(6) - 7$ $c = 24 - 7$ $c = 17$

Therefore, the value of $c$ is 17.

Q: Can I use a calculator to find the value of $c$ in the equation $c = 4d - 7$?

A: Yes, you can use a calculator to find the value of $c$ in the equation $c = 4d - 7$. Simply enter the values of $d$ and the equation into the calculator and press the "calculate" button.

Q: What is the difference between the equation $c = 4d - 7$ and the equation $c = 2d + 3$?

A: The equation $c = 4d - 7$ and the equation $c = 2d + 3$ are two different linear equations. The equation $c = 4d - 7$ states that $c$ is equal to four times the value of $d$, minus seven, while the equation $c = 2d + 3$ states that $c$ is equal to two times the value of $d$, plus three.

Conclusion

In this article, we have addressed some frequently asked questions (FAQs) related to finding the value of $c$ in the equation $c = 4d - 7$. We have discussed the importance of following the order of operations (PEMDAS) and provided examples of how to find the value of $c$ in the equation. By following these tips and practicing regularly, you can develop a deep understanding of algebra and apply it to real-world problems.

Additional Resources

For additional resources and practice problems, students can refer to the following:

• Khan Academy: Algebra
• Mathway: Algebra Solver
• Wolfram Alpha: Algebra Calculator

By following these resources and practicing regularly, students can develop a deep understanding of algebra and apply it to real-world problems.