Question

How do you solve `2(x=1)=3x-3`?

Answer 1

Solve: `2(x-1)=3x-3`

Remove the parentheses (by distributing the multiplication). Then Collect all terms involving the unknown (`x`) on one side and all other terms on the other side. Finish by dividing both sides by the coefficient of `x` (the number in front of `x`.

It looks like this:

`2(x-1)=3x-3`
`2x-2=3x-3`

Method 1, collect `x`-terms on the left.
`2x-2=3x-3`
(add `2` and subtract `3x` from both sides. Then divide)

`2x-3x=-3+2`
`-x=-1`

`(-x)/(-1)=(-1)/(-1)`

`x=1`

(There are other ways of convincing yourself that ix `-x=-1` is to be true, then we'll need to have `x=1`)

Method 2, avoid negatives in front of `x`
`2x-2=3x-3`

(add `3` and subtract `2x` on both sides)

`-2+3=3x-2x`
`1=x`
`x=1`