Solve Equation for y 6y-1.5x=8

Solve Equation for y 6y-1.5x=8

To solve the equation 6y – 1.5x = 8 for “y,” first add 1.5x to both sides to isolate the “6y” term:

6y = 8 + 1.5x

Then, divide both sides by 6 to find “y”:

y = (8 + 1.5x) / 6

So, the solution for “y” is y = (8 + 1.5x) / 6.

Isolating a Variable in a Multi-Variable Equation

Solving equations with multiple variables requires carefully applying algebra techniques to isolate the variable you aim to solve for. Let’s examine the step-by-step process for isolating y and solving the equation 6y – 1.5x = 8.

Group Terms by Variable

We first group all terms containing y together on one side and all x terms together on the other side:

6y – 1.5x = 8 6y = 1.5x + 8

Factor Out the y Variable

Factoring out the coefficient 6 from the y terms gives:

6y = 1.5x + 8 6(y) = 1.5x + 8

Divide Both Sides by the Coefficient

Dividing both sides by 6 isolates y:

6(y) = 1.5x + 8 (y) = (1.5x + 8)/6

Simplify the Right Side

Simplifying:

y = x/4 + 4/3

Therefore, the solution for y in terms of x is:

y = x/4 + 4/3

This isolates y on one side, allowing us to directly solve for its value when given an x input.

Checking your work is always key. We could substitute a sample x value in to verify y solves correctly using this new equation.

Methodically applying algebra allows isolating desired variables in multi-variable equations. This provides a powerful tool for determining unknowns in fields from physics to engineering. With practice, isolating variables becomes second nature.