Solving Linear Equations: Step-by-Step Guide with Practical Examples
Linear equations are a fundamental part of algebra and are used in a variety of real-world scenarios. In this article, we explore how to solve a linear equation of the form 6 ? x 9. We will walk through the process step-by-step, providing practical examples and explanations for each step.
Solving 6 - x 9
Method 1: Isolating x Using Addition
Start with the equation: 6 - x 9.
Subtract 6 from both sides to isolate the term with the variable: 6 - 6 - x 9 - 6 -x 3 Multiply both sides by -1 to solve for x: -1(-x) -1(3) x -3Method 2: Isolating x Using Subtraction and Division
Start with the equation: 6 - x 9.
Subtract 6 from both sides: 6 - 6 - x 9 - 6 -x 3 Divide both sides by -1: x -3Verification of the Solution
To verify that x -3 is the correct solution, substitute x back into the original equation:
6 - x 9
Step 1: Substitute x -3
6 - (-3) 9
Step 2: Simplify
6 3 9
9 9
The equation holds true, confirming that x -3 is indeed the solution.
Solving Similar Equations
Example 1: Solving 5x - 6 9
Given the equation 5x - 6 9, follow these steps:
Add 6 to both sides: 5x - 6 6 9 6 5x 15 Divide both sides by 5: x 15 / 5 x 3Example 2: Solving 6 - 2x 11
Given the equation 6 - 2x 11, follow these steps:
Subtract 6 from both sides: 6 - 2x - 6 11 - 6 -2x 5 Divide both sides by -2: x 5 / -2 x -2.5Verification: Substitute x -2.5 into the original equation:
6 - 2(-2.5) 11
6 5 11
11 11
The equation holds true, confirming that x -2.5 is the correct solution.
Conclusion
Mastering the art of solving linear equations is crucial when dealing with algebraic problems. By applying the steps of isolation and manipulation of variables, you can confidently solve a variety of linear equations. Whether it's 6 - x 9, 5x - 6 9, or 6 - 2x 11, the process remains consistent. Practice and patience are your greatest allies in this pursuit, and the website [AlgebraHelper]() provides additional resources to enhance your algebraic problem-solving skills.