Solving the Equation 2x 5 3x: A Step-by-Step Guide

Algebra is a fundamental part of mathematics, and understanding how to solve equations is crucial for many students. In this article, we will explore how to solve the equation 2x 5 3x. This step-by-step guide will help you understand different scenarios and solve it effectively. Let's dive into the details.

Case 1: 2x 5 3x

This is the most straightforward case to solve. Let's break it down:

Start with the equation: 2x 5 3x. Subtract 2x from both sides to move all the variable terms to one side: 2x 5 - 2x 3x - 2x Simplify to get: 5 x Therefore, the solution is: x 5

In this case, the absolute value (x) can indeed be positive, and the solution is straightforward.

Case 2: 2x 5 -3x

This scenario introduces a more complex element. Let's see how to solve it:

Start with the equation: 2x 5 -3x. Move all the variable terms to one side by adding 3x to both sides: 2x 5 3x -3x 3x Simplify to get: 5 -5x Divide both sides by -5 to isolate x: 5 / (-5) -5x / (-5) Simplify to get: -1 x Therefore, the solution is: x -1

However, it is important to note that in the context of mathematics, absolute values (x) cannot be negative. Thus, we must consider if x can indeed be -1. In this equation, we cannot have an absolute value of -1 since x represents a magnitude, which is always non-negative.

Therefore, our only valid solution is:

x 5

General Solution

To solve the equation 2x 5 3x step by step, follow these steps:

Start with the equation: 2x 5 3x. Subtract 2x from both sides to isolate the constant on one side: 2x 5 - 2x 3x - 2x Simplify to get: 5 x Therefore, the solution is: x 5

This method ensures that you always move the variable to one side and the constant to the other side, making the equation easier to solve.

Conclusion

In conclusion, solving equations like 2x 5 3x involves basic algebraic operations. The key is to isolate the variable on one side of the equation. By following these steps, you can solve various types of linear equations effectively. Understanding these methods will not only help in solving mathematical problems but also in real-world applications where algebraic equations are used.

Additional Resources

For further practice and understanding, consider exploring these resources: More algebraic equation practice problems Interactive online algebra tools and solvers Advanced algebra tutorials and resources