Solving Linear Equations: A Guide to Finding the Unknown

Linear equations are fundamental in mathematics and are crucial for understanding more complex mathematical concepts. They form the building blocks for solving a myriad of real-world problems. The simplest form of a linear equation is typically ax b c, where a, b, and c are constants and x is the variable whose value you are trying to determine. In this article, we will explore the step-by-step process of solving a linear equation to find the value of x in the given problem 6x 72.

Solution to the Equation: 6x 72

Let's break down the solution process for the equation 6x 72 as demonstrated by several methods. The core principle behind solving such equations is to isolate the variable x on one side of the equation.

Method 1: Direct Division
To solve for x in the equation 6x 72, you can divide both sides of the equation by 6, which simplifies the equation to isolate x: x 72/6 12 Therefore, x 12.

Method 2: Simplification
In the equation 6x - 2x 72, you can combine like terms by recognizing that 6x - 2x 4x. This simplifies the equation to see that 4x 72. Dividing both sides by 4 gives us x 72/4 18/2 9. However, the initial equation was 6x 72, so we have x 12.

Method 3: Division After Collecting Terms
If the equation is given as 6x - 2x 72, you can first combine like terms: 8x 72. Dividing both sides by 8 to isolate x results in:

However, as mentioned, the initial form of the equation is 6x 72, which leads us to x 12.

Conclusion: Why the Solution is X 12

It is essential to adhere to the principle that whatever operation you perform on one side of the equation must be performed on the other side to maintain equality. This ensures that the solution is accurate and consistent. Therefore, by applying the division correctly, we conclude that the solution to the equation 6x 72 is x 12.

To verify the solution, you can substitute x 12 back into the original equation:

6(12) 72

72 72

This confirms that the solution is indeed correct.

Always remember that solving equations requires a systematic approach to isolate the variable on one side. This guide has demonstrated the process through multiple methods, ultimately leading to the same solution: x 12.