Solving the Equation: 4 + 6/y = 5/2

In this article, we will explore the process of solving the equation 4 + 6/y = 5/2 for the variable y. This type of equation is commonly encountered in high school mathematics and is an essential skill for students to master.

Step 1: Understand the Equation

The given equation is 4 + 6/y = 5/2. This is an algebraic equation with one variable, y, and we need to find the value of y that satisfies the equation.

Step 2: Isolate the Variable

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

1. Subtract 4 from both sides of the equation: 4 + 6/y = 5/2 6/y = 5/2 - 4 6/y = -3/2

2. Multiply both sides of the equation by y to eliminate the fraction: 6/y = -3/2 6 = -3y/2

3. Multiply both sides of the equation by -2 to isolate y: 6 = -3y/2 -12 = 3y y = -4

Step 3: Check the Solution

To ensure that the solution is correct, we can substitute the value of y back into the original equation and verify that the equation is satisfied.

4 + 6/(-4) = 5/2 4 + (-1.5) = 5/2 2.5 = 2.5

The equation is satisfied, so the solution y = -4 is correct.

Conclusion

In this article, we have walked through the step-by-step process of solving the equation 4 + 6/y = 5/2 for the variable y. By isolating the variable and performing the necessary algebraic manipulations, we arrived at the solution y = -4. This type of equation-solving skill is essential for high school mathematics students and can be applied to a wide range of algebraic problems.