Solve C/-6=4 Equation Step-by-Step Guide For Beginners

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In this comprehensive guide, we will solve the equation C/-6 = 4 for the variable C. This is a fundamental algebraic problem that requires understanding basic arithmetic operations and the concept of isolating a variable. Whether you're a student learning algebra for the first time or someone looking to refresh your skills, this guide will provide a clear and concise explanation of the solution process. We will break down each step, ensuring you grasp the underlying principles and can confidently tackle similar problems in the future.

Understanding the Equation

Before diving into the solution, let's first understand the equation we're dealing with: C/-6 = 4. This equation states that when the variable C is divided by -6, the result is 4. Our goal is to find the value of C that makes this statement true. To do this, we need to isolate C on one side of the equation. Isolating a variable means getting it by itself on one side of the equation, with all other terms and constants on the other side. This is achieved by performing inverse operations, which are operations that undo each other. For example, addition and subtraction are inverse operations, and multiplication and division are inverse operations. In our equation, C is being divided by -6. To isolate C, we need to perform the inverse operation of division, which is multiplication.

Step-by-Step Solution

Now, let's walk through the step-by-step solution to solve for C:

Step 1: Multiply both sides of the equation by -6

To isolate C, we need to get rid of the -6 in the denominator. To do this, we multiply both sides of the equation by -6. This is a crucial step, as it maintains the equality of the equation. Whatever operation we perform on one side, we must perform on the other side to keep the equation balanced.

C/-6 = 4

Multiply both sides by -6:

(-6) * (C/-6) = 4 * (-6)

Step 2: Simplify the equation

On the left side of the equation, the -6 in the numerator and the -6 in the denominator cancel each other out, leaving us with just C. On the right side, we multiply 4 by -6, which gives us -24.

C = -24

Step 3: State the solution

Therefore, the solution to the equation C/-6 = 4 is C = -24. This means that if we substitute -24 for C in the original equation, the equation will be true. Let's verify this by plugging -24 back into the original equation:

(-24)/-6 = 4

4 = 4

The equation holds true, so our solution is correct.

Verification of the Solution

It's always a good practice to verify your solution by substituting it back into the original equation. This helps to ensure that you haven't made any mistakes in your calculations. In our case, we substituted C = -24 back into the equation C/-6 = 4 and found that it held true. This confirms that our solution is correct.

Common Mistakes to Avoid

When solving equations, it's easy to make mistakes if you're not careful. Here are some common mistakes to avoid:

  • Not performing the same operation on both sides: Remember, whatever operation you perform on one side of the equation, you must perform on the other side to maintain equality. For example, if you multiply the left side by -6, you must also multiply the right side by -6.
  • Incorrectly applying inverse operations: Make sure you're using the correct inverse operation to isolate the variable. For example, if the variable is being divided, you need to multiply, not divide.
  • Arithmetic errors: Simple arithmetic errors can lead to incorrect solutions. Double-check your calculations to ensure accuracy.
  • Forgetting the negative sign: When dealing with negative numbers, it's easy to forget the negative sign. Pay close attention to the signs and make sure you're applying them correctly.

Practice Problems

To solidify your understanding, here are some practice problems similar to the one we just solved:

  1. x/-3 = 5
  2. y/2 = -7
  3. z/-4 = -2

Try solving these problems on your own, using the steps outlined in this guide. Once you've solved them, you can check your answers by substituting them back into the original equations.

Real-World Applications

Solving equations for variables is a fundamental skill in mathematics that has numerous real-world applications. Here are a few examples:

  • Finance: Calculating interest rates, loan payments, or investment returns often involves solving equations.
  • Physics: Many physics formulas are equations that need to be solved for specific variables, such as velocity, acceleration, or force.
  • Engineering: Engineers use equations to design structures, circuits, and other systems.
  • Everyday life: Even in everyday situations, we often use equations to solve problems, such as calculating the cost of items on sale or determining the amount of ingredients needed for a recipe.

Conclusion

In this guide, we've walked through the process of solving the equation C/-6 = 4 for the variable C. We've covered the importance of isolating the variable, the use of inverse operations, and the verification of the solution. By following the steps outlined in this guide and practicing similar problems, you can develop your algebraic skills and confidently solve a wide range of equations. Remember, consistent practice is key to mastering algebra and other mathematical concepts.

This equation, C/-6 = 4, serves as a foundational example for more complex algebraic problems. Understanding how to isolate variables and apply inverse operations is crucial for success in higher-level mathematics. As you progress in your mathematical journey, you'll encounter more intricate equations involving multiple variables and operations. However, the fundamental principles we've discussed here will remain relevant and essential.

The ability to solve equations is not just a valuable skill in mathematics; it's also a valuable skill in life. It helps you develop problem-solving abilities, critical thinking skills, and the ability to approach challenges in a systematic way. Whether you're balancing your budget, planning a project, or making important decisions, the skills you learn from solving equations can be applied in various aspects of your life. Therefore, mastering these fundamental concepts is an investment in your future success.

So, continue practicing, exploring different types of equations, and challenging yourself to improve your mathematical skills. The more you practice, the more confident and proficient you'll become. And remember, mathematics is not just about numbers and formulas; it's about logical thinking, problem-solving, and understanding the world around us.

Solve the equation C / -6 = 4 for the variable C.

Solve C/-6=4 Equation Step-by-Step Guide for Beginners