Solving Algebraic Equations: A Step-by-Step Guide

Understanding and solving algebraic equations is a fundamental part of mathematics. In this article, we will explore the process of solving a specific equation, 5x - 2x - 66 4x6, through a detailed step-by-step guide. This will help you grasp the techniques needed to tackle similar problems with ease.

Understanding the Equation

Let's begin with the given algebraic equation:

5x - 2x - 66 4x6

Step-by-Step Solution

Step 1: Simplify the Equation

The first step in solving any equation is to simplify it. We can start by simplifying the left-hand side of the equation:

5x - 2x - 66 4x6

Combining like terms on the left-hand side:

3x - 66 4x6

Step 2: Group Like Terms

Next, we will group the like terms together. Notice that 4x6 simplifies to 24:

3x - 66 24x

Step 3: Isolate the Variable

To isolate the variable x, we need to get all terms involving x on one side of the equation and constants on the other side. First, subtract 3x from both sides:

-66 24x - 3x

-66 21x

Now, we have all terms with x on the right-hand side and the constant on the left-hand side.

Step 4: Solve for x

To solve for x, we need to isolate it further. Divide both sides by 21:

x -66 / 21

Perform the division:

x -6

Conclusion

Therefore, the solution to the equation 5x - 2x - 66 4x6 is:

x -6

Further Examples and Practice

Here are some additional examples to help you practice solving similar algebraic equations:

Example 1:

Solve for x:

3x 4 2x - 10

Start by moving all terms involving x to one side and constants to the other:

3x - 2x -10 - 4

x -14

x -14

Example 2:

Solve for x:

7x - 3x 8 2x 10

Simplify and group like terms:

4x 8 2x 10

Subtract 2x from both sides:

2x 8 10

Subtract 8 from both sides:

2x 2

Divide by 2:

x 1

x 1

By following these steps and practicing with different equations, you can become proficient in solving algebraic equations. This will not only improve your mathematical skills but also enhance your problem-solving abilities in various real-world applications.

Related Keywords: algebraic equations, solving equations, step-by-step solutions