## 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.

GEG Calculators is a comprehensive online platform that offers a wide range of calculators to cater to various needs. With over 300 calculators covering finance, health, science, mathematics, and more, GEG Calculators provides users with accurate and convenient tools for everyday calculations. The website’s user-friendly interface ensures easy navigation and accessibility, making it suitable for people from all walks of life. Whether it’s financial planning, health assessments, or educational purposes, GEG Calculators has a calculator to suit every requirement. With its reliable and up-to-date calculations, GEG Calculators has become a go-to resource for individuals, professionals, and students seeking quick and precise results for their calculations.