Hi Lisa,
I'm going to do a slightly different problem to help you with the one you have. I am going to solve for x where
8  3x = 2(x  1)
First I note that, on the right side, both terms inside the parentheses are to be multiplied by 2. That is
2(x  1) = 2 x  2 1 = 2x  2
Thus the equation can be rewritten
8  3x = 2x  2
Now I see the equation as a balance with 8  3x on one side of the balance and 2x  2 on the other side. I want to manipulate both sides, keeping them in balance, and end with an equation of the form
x = some number
Hence I want x alone on the left and a number, with no x's on the right.
To remove all the x's from the right side and still maintain the balance I can add 2x to both sides. Thus
8  3x = 2x  2
8  3x 2x = 2x  2 2x
8  5x = 2
Removing the 8 from the left side is the next step. I do this by adding 8 to both sides.
8  5x = 2
8  5x 8 = 2 8
5x = 10
Almost done. Divide both sides by 5 to get
5x = 10
^{5x}/_{5} = ^{10}/_{5}
x = 2
So here is my neat solution
8  3x = 2(x  1)
8  3x = 2x  2
8  3x  8 = 2x  2  8
3x = 2x  10
3x  2x = 2x  10  2x
5x = 10
^{5x}/_{5} = ^{10}/_{5}
x = 2
Penny
