Solving the Equation 3-x 6 and Related Problems

Linear equations are fundamental in algebra and frequently encountered in various real-world scenarios. In this article, we will solve a specific equation, 3-x 6, and explore related problems step-by-step. This guide will help you understand the process of solving such equations, enhancing your algebra skills and providing valuable insights for Google search optimization.

Introduction to Linear Equations

A linear equation in one variable is an equation that can be written in the form ax b 0, where a and b are constants, and a ≠ 0. The most straightforward case is where a is equal to 1, such as in the equation we will solve: 3-x 6.

Solving 3-x 6

Let's begin with solving the equation 3-x 6 using different methods. We will detail the process and explain each step to ensure clarity.

Method 1: Basic Algebraic Manipulation

Start with the equation: 3 - x 6 Subtract 3 from both sides: -x 3 Multiply both sides by -1 to isolate x: x -3 Verification: 3 - (-3) 6

Method 2: Clearing the Denominator

Multiply both sides of the equation by 4 (to clear the denominator):
4(3 - x/4) 4(6) Simplify: 12 - x 24 Add x to both sides and subtract 24 from both sides: -x 12 Multiply both sides by -1: x -12 Verification: 3 - -12/4 3 - (-3) 3 3 6

Method 3: Another Approach

Multiply both sides of the equation by 4: 4(3 - x/4) 4(6) Simplify: 12 - x 24 Add x to both sides and subtract 24 from both sides: -4x - 3x 24 - 12 Combine like terms: -7x 12 Solve for x: x -12/7 Verification: 3 - -12/7 3 12/7 21/7 12/7 33/7 4.7143 6.7143 (approximatly)

Conclusion

By following these detailed steps, you can solve linear equations effectively. The methods we discussed are not only applicable to the specific problem at hand but also provide a foundation for solving other linear equations. Whether you are a student, a professional, or someone who needs to brush up on their algebra skills, understanding these techniques is essential.

Related Problems for Practice

To further solidify your understanding, here are a few related linear equations for practice:

2x 5 11 4x - 3 7 6 - 2x 10

Work through these problems using the methods we discussed. For more detailed explanations and additional practice, consider consulting a textbook or online resources on algebra.

Conclusion

Solving linear equations like 3-x 6 is an essential skill in algebra. By mastering this skill, you can handle more complex equations and solve real-world problems more effectively. Whether you are studying for a math test, preparing for a job interview, or simply enhancing your problem-solving abilities, understanding how to solve these equations will serve you well.

If you have any questions or need additional assistance, feel free to explore more resources online or reach out to a math tutor. Keep practicing and improving your algebra skills!