5(x-4)=3(2-3x) name: lisa Level of question: ks3 level 6 who is asking the question : pupil 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