Solve 6 X + C = K 6x + C = K 6 X + C = K For X X X .A. X = 6 ( K − C X = 6(k - C X = 6 ( K − C ] B. X = K − C 6 X = \frac{k - C}{6} X = 6 K − C ​ C. X = K + C 6 X = \frac{k + C}{6} X = 6 K + C ​ D. X = 6 ( K + C X = 6(k + C X = 6 ( K + C ]

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill to master. In this article, we will focus on solving a specific type of linear equation, namely $6x + c = k$, for the variable $x$. We will explore the different methods and techniques used to solve this equation and provide step-by-step examples to illustrate the process.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation $6x + c = k$

The equation $6x + c = k$ is a linear equation in which the coefficient of $x$ is 6, and the constant term is $c$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. This can be done by subtracting $c$ from both sides of the equation and then dividing both sides by 6.

Step-by-Step Solution

To solve the equation $6x + c = k$ for $x$, follow these steps:

1. Subtract $c$ from both sides: This will eliminate the constant term $c$ from the left side of the equation.

   $6x + c - c = k - c$

   Simplifying the left side, we get:

   $6x = k - c$

2. Divide both sides by 6: This will isolate the variable $x$ on the left side of the equation.

   $\frac{6x}{6} = \frac{k - c}{6}$

   Simplifying the left side, we get:

   $x = \frac{k - c}{6}$

Conclusion

In conclusion, solving the equation $6x + c = k$ for $x$ involves subtracting $c$ from both sides and then dividing both sides by 6. This results in the solution $x = \frac{k - c}{6}$. It is essential to remember that when solving linear equations, the order of operations must be followed, and the variable must be isolated on one side of the equation.

Answer Key

The correct answer is:

• A. $x = 6(k - c)$ is incorrect.
• B. $x = \frac{k - c}{6}$ is correct.
• C. $x = \frac{k + c}{6}$ is incorrect.
• D. $x = 6(k + c)$ is incorrect.

Additional Examples

To reinforce your understanding of solving linear equations, try the following examples:

• Solve the equation $3x + 2 = 5$ for $x$.
• Solve the equation $2x - 4 = 6$ for $x$.
• Solve the equation $x + 3 = 7$ for $x$.

By practicing these examples, you will become more confident in your ability to solve linear equations and apply this skill to a wide range of mathematical problems.

Tips and Tricks

When solving linear equations, remember to:

• Follow the order of operations (PEMDAS).
• Isolate the variable on one side of the equation.
• Use inverse operations to eliminate the coefficient of the variable.
• Check your solution by plugging it back into the original equation.

By following these tips and tricks, you will become a master of solving linear equations and be able to tackle even the most challenging problems with confidence.

Conclusion

Introduction

In our previous article, we explored the concept of solving linear equations, with a focus on the equation $6x + c = k$. We provided a step-by-step guide on how to solve this equation and offered additional examples to reinforce your understanding. In this article, we will address some of the most frequently asked questions about solving linear equations.

Q&A

Q: What is the first step in solving a linear equation?

A: The first step in solving a linear equation is to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: How do I know which operation to perform first?

A: To determine which operation to perform first, follow the order of operations (PEMDAS):

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

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable(s) is 2.

Q: Can I use the same method to solve all linear equations?

A: While the method for solving linear equations is similar, the specific steps may vary depending on the equation. For example, if the equation has a coefficient of 0, you may need to use a different method to solve it.

Q: How do I check my solution?

A: To check your solution, plug it back into the original equation and verify that it is true. If the solution satisfies the equation, then it is correct.

Q: What if I get stuck or make a mistake?

A: If you get stuck or make a mistake, don't worry! Take a step back and re-evaluate the equation. Check your work and make sure you are following the correct steps. If you are still having trouble, consider seeking help from a teacher, tutor, or classmate.

Q: Can I use technology to solve linear equations?

A: Yes, you can use technology to solve linear equations. Many graphing calculators and computer algebra systems (CAS) can solve linear equations and provide step-by-step solutions.

Q: Are there any real-world applications of solving linear equations?

A: Yes, solving linear equations has many real-world applications, including:

• Physics: Solving linear equations is used to model the motion of objects and predict their trajectories.
• Engineering: Solving linear equations is used to design and optimize systems, such as bridges and buildings.
• Economics: Solving linear equations is used to model economic systems and make predictions about future trends.
• Computer Science: Solving linear equations is used in computer graphics and game development to create realistic simulations.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it has many real-world applications. By following the steps outlined in this article and practicing with additional examples, you will become proficient in solving linear equations and be able to apply this skill to a wide range of mathematical problems. Remember to always follow the order of operations, isolate the variable, and use inverse operations to eliminate the coefficient of the variable. With practice and dedication, you will become a master of solving linear equations and be able to tackle even the most challenging problems with confidence.

Additional Resources

For more information on solving linear equations, check out the following resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations
• MIT OpenCourseWare: Linear Algebra

By taking advantage of these resources, you will be able to deepen your understanding of solving linear equations and apply this skill to a wide range of mathematical problems.