Solving Equations: A Step-by-Step Guide to 6x 12

In this comprehensive guide, we'll walk you through the process of solving the equation 6x 12. This is a fundamental task in algebra that helps in developing a strong mathematical foundation. Solutions to such equations are essential skills for students and professionals in various fields, from engineering to finance.

Understanding the Equation

The equation we aim to solve is 6x 12, where x is an unknown variable. Our goal is to isolate the variable x on one side of the equation to find its value.

Breaking Down the Solution

Step 1: Identify the Equation

Let's start by clearly identifying the equation we need to solve:

6x  12

Step 2: Isolate the Variable

To isolate x, we need to divide both sides of the equation by the coefficient of x, which is 6. This division will result in x being alone on the left side of the equation:

6x 12 x 12/6 x 2

Step 3: Simplify the Solution

By performing the division, we obtain:

x 2

Verification

To ensure the correctness of our solution, we can substitute x 2 back into the original equation:

6(2)  12

Indeed, 6 multiplied by 2 equals 12, confirming our solution is correct.

Practical Applications

The ability to solve equations like 6x 12 is not just for academic purposes. It has real-world applications in various fields. For example, in engineering, you might need to calculate the dimensions of a structure. In finance, solving such equations can help determine interest rates or financial goals. In science, these equations might represent a chemical reaction rate or a physical phenomenon.

Conclusion

Understanding how to solve equations such as 6x 12 is a fundamental skill in algebra, essential for solving more complex equations and applying algebra in various fields. The process of solving this equation, 6x 12, involves isolating the variable by applying the same mathematical operations to both sides of the equation. This guide has provided a clear step-by-step method to solve the equation and verify the solution.

Frequently Asked Questions

What is the solution to 6x 12?

The solution to the equation 6x 12 is x 2.

How do I verify if my solution is correct?

To verify your solution, substitute the value of x back into the original equation and check if both sides are equal. In this case, substituting x 2 into 6x 12 gives 6(2) 12, which is correct.

What is algebra used for in real life?

Algebra is used in various real-life applications, including financial analysis, engineering design, scientific research, and problem-solving in everyday situations. It helps in making predictions, analyzing data, and finding solutions to complex problems.