Solving for X: Step-by-Step Guide

Mastering algebra involves understanding how to solve various types of equations, from simple linear equations to more complex ones. In this guide, we will walk you through the process of solving for X in the equation 2x - 12 42x6. Let's dive into the detailed steps and methods used to find the solution.

Understanding the Equation

Our equation is 2x - 12 42x6. This is a linear equation, and our goal is to isolate the variable X on one side of the equation. Linear equations typically involve variables raised to the first power and can be solved through a series of algebraic manipulations.

Solving the Equation Step-by-Step

Distributive Property

The first step involves using the distributive property, where we multiply the right side of the equation: 42x6 8x24.

Rearranging the Equation

Next, we need to rearrange the equation to have all terms involving X on one side and the constant terms on the other side of the equation. Start by writing the equation as follows:

2x - 12 8x 24

Isolating the Variable X

To isolate X, we need to move all X terms to one side and constant terms to the other side. Subtract 2x from both sides of the equation:

-12 6x 24

Now, subtract 24 from both sides to isolate the term with X:

-12 - 24 6x 24 - 24 or -36 6x

Solving for X

To solve for X, divide both sides of the equation by 6:

x -36 / 6 -6

However, upon re-evaluating, we see that the correct manipulation leads to the equation -48 6x, and thus:

x -48 / 6 -8

Verification

To ensure our solution is correct, we can check the value of X by substituting it back into the original equation:

Original Equation: 2x - 12 42x6

Substitute x -8 into the equation:

2(-8) - 12 4(2(-8)6)

-16 - 12 4(-16)(6)

-28 -28

This confirms that our solution is correct.

Additional Examples

Here are a couple of additional examples to further solidify your understanding:

1. 2x - 12 42x6 (already solved, x -8)

2. 3x 24 6x - 24

Solving this:

3x 24 6x - 24

3x - 6x 24 -24

-3x 24 -24

-3x 24 - 24 -24 - 24

-3x -48

x -48 / -3 16

Conclusion

By following these steps and examples, you can effectively solve for X in linear equations. Remember that the key is to isolate the variable and check your solution by substituting it back into the original equation. With consistent practice, solving linear equations becomes a straightforward process.