Solving the Equation x/5 4 7x - 6: A Comprehensive Guide

Are you struggling to solve mathematical equations, particularly linear equations? In this article, we will walk you through the process of solving the equation x/5 4 7x - 6. This step-by-step guide will help you understand the problem and provide a clear solution, making it easier for you to tackle similar algebraic problems in the future.

Understanding the Problem

The given equation is x/5 4 7x - 6. This is a linear equation where we need to find the value of the variable x. To solve this equation, we will follow a series of algebraic steps to isolate the variable x.

Solving the Equation Step-by-Step

Let's start by simplifying the equation:

Multiply both sides of the equation by 5 to eliminate the fraction: Multiply both sides of the equation by 5: (x/5 4) * 5 (7x - 6) * 5 This simplifies to: x 20 35x - 30

Now, let's isolate the variable x on one side of the equation:

Move all terms with x to one side of the equation: x - 35x -20 - 30 This simplifies to: -34x -50

Now, we need to isolate x by dividing both sides by -34:

-34x -50 x -50 / -34 This simplifies to: x 50 / 34 Finally, simplify the fraction: x 25 / 17

Verifying the Solution

To ensure our solution is correct, let's verify it by substituting x 25 / 17 into the original equation:

Left side: x/5 4 (25/17) / 5 4 25/85 4 (25 340) / 85 365 / 85 Right side: 7x - 6 7(25/17) - 6 175/17 - 6 (175 - 102) / 17 73 / 17 Simplify both sides: (365 / 85) (73 / 17) The left side equals the right side, confirming our solution is correct.

Conclusion

Solving the equation x/5 4 7x - 6 involves a series of algebraic steps. By multiplying both sides by 5, isolating the variable, and simplifying the fraction, we arrive at the solution x 25 / 17. This step-by-step process not only solves the equation but also provides a clear understanding of the problem-solving methodology. Practice similar problems to enhance your algebraic skills and deepen your understanding of linear equations.