What is the solution to the equation 5y - 2 = 3y + 6?

To solve the equation (5y - 2 = 3y + 6), the goal is to isolate the variable (y). Start by moving all terms involving (y) to one side of the equation and the constant terms to the other side.

Begin by subtracting (3y) from both sides:

[ 5y - 3y - 2 = 6 ]

This simplifies to:

[ 2y - 2 = 6 ]

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

[ 2y - 2 + 2 = 6 + 2 ]

This simplifies to:

[ 2y = 8 ]

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

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

Thus, the solution to the equation is (y = 4). This confirms that the correct choice corresponds to (y = 4), as it is the value that satisfies the original equation when substituted back in. Making sure to check the solution by substituting (4) back into the