Solving the Linear Equation: 2x-3-76-5x1
Linear equations are a fundamental part of algebra, often encountered in high school mathematics and real-world applications. This article aims to provide a step-by-step guide to solving the linear equation 2x-3-76-5x1. We will break down the process, ensuring that you understand each step of the solution. Additionally, we will include a comprehensive explanation of the algebraic principles used in solving such equations.
Understanding the Equation and Initial Steps
The given equation is:
2x - 3 - 7 6 - 5x1
The first step is to simplify the equation by removing any unnecessary elements and combining like terms. In this case, the equation can be rewritten as:
2x - 6 - 7 6 - 5x - 5
Combining the constants on the left side and the constants on the right side of the equation, we get:
2x - 13 6 - 5x - 5
Further simplification on the right side of the equation yields:
2x - 13 1 - 5x
Solving the Equation Step by Step
To solve the equation, we need to isolate the variable x. Here are the steps:
Combine like terms on both sides of the equation: Add 5x to both sides to isolate the x terms on one side: Add 13 to both sides to isolate the constant term on the other side: Divide both sides by 7 to solve for x:Step 1: Combine Like Terms
The equation is simplified as:
2x - 13 1 - 5x
Step 2: Add 5x to Both Sides
Adding 5x to both sides:
2x 5x - 13 1
This simplifies to:
7x - 13 1
Step 3: Add 13 to Both Sides
Adding 13 to both sides to isolate the x term:
7x 1 13
This simplifies to:
7x 14
Step 4: Divide Both Sides by 7
The final step is to divide both sides by 7:
x 14 / 7
This gives us:
x 2
Conclusion
In conclusion, the solution to the equation 2x - 3 - 7 6 - 5x1 is x 2. By following these detailed steps, you can solve similar linear equations with confidence. If you have any questions or need further clarification, feel free to ask. Happy problem-solving!