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