Solving the Equation 2x - 1 -3: A Comprehensive Guide
When dealing with algebraic expressions, understanding how to solve simple linear equations is a fundamental skill. This guide will walk you through the process of solving the equation 2x - 1 -3. We'll break it down step by step and explain the logic behind each move. This guide is perfect for both beginners and those looking to refresh their algebra skills.
What is 2x - 1 -3?
The equation 2x - 1 -3 is a simple linear equation of the form ax b c, where a, b, and c are constants, and x is the variable we want to solve for. In this case, a 2, b -1, and c -3. Let's dive into the solution process.
Solving the Equation 2x - 1 -3
To solve for x, we need to isolate x on one side of the equation. The process involves performing the same operations on both sides of the equation to maintain equality. Let's break it down:
Starting with the equation:
2x - 1 -3
The first step is to get rid of the -1 on the left side. We do this by adding 1 to both sides of the equation.
2x - 1 1 -3 1
Simplifying both sides:
2x -2
Now, to solve for x, we need to divide both sides by 2.
2x ÷ 2 -2 ÷ 2
Simplifying:
x -0.5
To verify the solution, substitute x -0.5 back into the original equation:
2(-0.5) - 1 -3
Multiplying and simplifying:
-1 - 1 -3
This confirms that -3 is the correct result, so our solution is verified.
Calculations
To further illustrate the calculation, let's break it down with a detailed step-by-step process:
2x - 1 -3 2x - 2 -3 2x -32 2x -1 2x ÷ 2 -1 ÷ 2 x -0.5Perform the final step:
2(-0.5) - 1 -3
Multiplying and simplifying:
-1 - 1 -3
Conclusion
By following these steps, we have successfully solved the equation 2x - 1 -3. The solution is x -0.5. Understanding the process of isolating the variable and performing the same operations on both sides of the equation is crucial for solving more complex algebraic problems. Practice these steps with different equations to build your algebra skills.