Determining if 3 is a Solution to 6x - 7 12

In the world of algebra, determining whether a given value is a solution to a given equation is a fundamental skill. This article will explore a specific example where we need to verify if the number 3 is indeed a solution to the equation 6x - 7 12. We'll delve into the process step-by-step to ensure clarity and understanding of the concept.

Introduction to Algebraic Equations

Algebraic equations are mathematical statements that show the equality between two expressions. They are often used to model real-world scenarios and solve problems involving unknown values, known as variables (usually denoted by letters such as x, y, or z).

Given Equation and Initial Assumption

Consider the following equation:

6x - 7 12

Let's assume that x 3 is a solution to this equation. We will substitute this value into the equation and check if it holds true.

Step-by-Step Verification

Step 1: Substitute x 3 into the equation 6x - 7 12.

6(3) - 7 12

Step 2: Perform the multiplication.

18 - 7 12

Step 3: Perform the subtraction.

11 12

Step 4: Compare the left-hand side (LHS) with the right-hand side (RHS) of the equation.

11 ≠ 12

Since 11 is not equal to 12, we can conclude that x 3 is not a solution to the equation 6x - 7 12.

Understanding the Result

The process of substituting a value into an equation and comparing the results helps us determine if the chosen value is a solution. In this case, we found that x 3 does not satisfy the equation, indicating that it is not a solution.

Conclusion

In conclusion, the value x 3 does not solve the equation 6x - 7 12. The step-by-step verification process clearly shows that substituting x 3 into the equation leads to a contradiction, confirming that 3 is not a solution to the equation.

Additional Insights and Recommendations

This example reinforces the importance of algebraic manipulation and verification techniques in solving equations. It also illustrates the significance of performing each step methodically to ensure accuracy.

For further practice, try solving similar equations by substituting different values and verifying the results. This will help solidify your understanding of the concepts involved and improve your algebraic problem-solving skills.