Solving the Equation: 3x - x7 25

Solving the Equation: 3x - x7 25

Solving equations is a fundamental skill in algebra, and it's crucial for students to understand the processes and rules involved. In this article, we will walk through the steps to solve the equation 3x - x - 7 25. This type of problem requires the application of the distributive property, algebraic simplification, and the inverse operations principle.

Solving Algebraic Equations: A Step-by-Step Guide

To solve the equation 3x - x - 7 25, let's break it down into manageable steps using a systematic approach.

Step 1: Simplifying the Equation

First, let's simplify the left side of the equation.

Original Equation: 3x - x - 7 25 Combine like terms (3x - x): Simplified Equation: 2x - 7 25

Step 2: Using the Inverse Operations Principle

Next, we need to isolate the variable x. To do this, we will use the inverse operations principle, which states that we can perform the same operation on both sides of the equation to keep it balanced.

First, we add 7 to both sides of the equation to eliminate the -7 on the left side: 2x - 7 7 25 7 2x 32 Now, we divide both sides by 2 to isolate x: 2x / 2 32 / 2 x 16

Step 3: Verifying the Solution

To ensure our solution is correct, we can substitute x 16 back into the original equation and check if it holds true.

Substitute x 16 into 3x - x - 7 25: 3(16) - 16 - 7 25 48 - 16 - 7 25 48 - 23 25 25 25

The equation is balanced, confirming that our solution is correct. Therefore, the value of x is 16.

Conclusion

By following these steps, we have successfully solved the equation 3x - x - 7 25. The key principles used were the distributive property, combining like terms, using the inverse operations principle, and verifying the solution. Understanding these concepts will greatly enhance your ability to tackle similar algebraic problems in the future.

Additional Resources

For further practice and in-depth learning, consider exploring additional resources such as interactive algebra tutorials, online math quizzes, and step-by-step guides on solving algebraic equations.

Key Takeaways

Understanding the distributive property is essential for simplifying equations. Combine like terms to simplify the equation before solving. The inverse operations principle is a powerful tool for isolating variables. Always verify your solution by substituting it back into the original equation.