Hi Terri,
The task is to solve for x which means you are to manipulate the equation, at ever step ensuring that the equality is still valid, and end with an equation
x = some number.
So you want x alone on the left of the equality and a number on the right.
To ensure that the equality remains valid at each step you can add or subtract the same amount to each side or you can multiply each side by the same number. You can also divide both sides by the same number but you need to ensure that you don't divide by zero. I am going to illustrate with a different example.
Solve for x: (4x+3)/5 x/2 = (5x2)/10
My first thought is to eliminate the fractions. I can do this in two ways. One is to take the two fractions on the left and find a common denominator and simplify from there. A technique I think is quicker is to multiply both sides by 10. This gives
(4x+3)/5 x/2 = (5x2)/10
10[(4x+3)/5 x/2] = 10[(5x2)/10]
10[(4x+3)/5]  10[x/2] = 5x  2
2(4x + 3)  5(x) = 5x  2
8x + 6  5x = 5x  2
3x + 6 = 5x  2
I don't want an x on the right side so subtract 5x from both sides.
3x + 6 = 5x  2
3x + 6 5x = 5x  2 5x
2x + 6 = 2
We are almost there. I don't want the 6 on the left so subtract 6 from both sides
2x + 6 = 2
2x + 6  6 = 2 6
2x = 8
Finally divide both sides by 2 to get
2x = 8
2x/2 = 8/2
x = 4
Now try your problem,
Penny
