Solving the Linear Equation: (5x - 140)/x = -15

In this article, we will explore the step-by-step process of solving the linear equation: (5x - 140)/x = -15. This type of equation is commonly encountered in high school mathematics, and understanding the techniques to solve it is essential for students to develop their algebraic problem-solving skills.

Step 1: Understand the Equation

The equation (5x - 140)/x = -15 is a linear equation in one variable, x. The left-hand side of the equation is a rational expression, where the numerator is 5x - 140 and the denominator is x. The right-hand side of the equation is a constant, -15.

Step 2: Isolate the Variable

To solve for x, we need to isolate the variable on one side of the equation. We can do this by performing the following steps:

1. Multiply both sides of the equation by x to eliminate the fraction: (5x - 140)/x = -15 x(5x - 140)/x = x(-15) 5x - 140 = -15x

2. Combine like terms on the left-hand side: 5x - 140 = -15x 20x = 140

3. Divide both sides by 20 to isolate x: 20x = 140 x = 140/20 x = 7

Step 3: Check the Solution

To verify that the solution is correct, we can substitute the value of x back into the original equation and check if the equation is true.

Substituting x = 7 into the original equation: (5(7) - 140)/7 = -15 (35 - 140)/7 = -15 -105/7 = -15 -15 = -15 (The equation is true, so the solution is correct.)

Conclusion

In this article, we have demonstrated the step-by-step process of solving the linear equation (5x - 140)/x = -15. By isolating the variable and performing the necessary algebraic operations, we were able to find the solution x = 7. Remember, the key to solving these types of equations is to understand the underlying concepts, follow the steps carefully, and always verify the solution by substituting it back into the original equation.