Solve the equation 3y+6=y-2 for y.

The task is to
solve

3y+6=y-2

We first try to group
terms containing the unknown ("y" in this case) to one side of the equation and those that do not
contain the unknown to the other side.

With that in mind, we have to
abide by some rules pertaining to algebraic manipulation.  Simply put, the rule can be sum up as
"what ever operation you do on one side, do it equally on the
other"

First, we want to be able to move the y on the RHS (Right
hand side) to the left.  So we minus y on both side:

3y +6
-y = y -2
-y

We then
get

2y +6 = -2

Now, we want to get rid
of the 6 on the LHS (left hand side).  We minus 6 on both sides:

2y
+6 -6 = -2
-6

Which
yield

2y = -8

Now the final step.  We
want to find y.  So we divide both sides by 2:

2y
/2 =  -8
/2

and we
get

y =
-4

The required answer is
y=-4

___

Counter
checking

We can put this newly found value of y back
into the original equation to see if it works out:

LHS= 3(-4)+6 =
-6

RHS= (-4)-2 = -6

LHS=RHS.  Hence the
answer found was correct.