If 5y - 2 = 3y + 6, what is the value of y?

To solve the equation (5y - 2 = 3y + 6) for (y), the steps involve isolating the variable.

First, start by rearranging the equation to group the (y)-terms on one side. This can be done by subtracting (3y) from both sides:

[

5y - 3y - 2 = 6

]

This simplifies to:

[

2y - 2 = 6

]

Next, add (2) to both sides of the equation to further isolate the term containing (y):

[

2y - 2 + 2 = 6 + 2

]

This gives:

[

2y = 8

]

Finally, divide both sides by (2) to solve for (y):

[

y = \frac{8}{2} = 4

]

Thus, the value of (y) is (4). This calculation correctly follows algebraic principles of solving linear equations by isolating the variable step by step.