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

Mar 25, 2015

Solve: $2 \left(x - 1\right) = 3 x - 3$

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:

$2 \left(x - 1\right) = 3 x - 3$
$2 x - 2 = 3 x - 3$

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

$2 x - 3 x = - 3 + 2$
$- x = - 1$

$\frac{- x}{- 1} = \frac{- 1}{- 1}$

$x = 1$

(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 $x$
$2 x - 2 = 3 x - 3$

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

$- 2 + 3 = 3 x - 2 x$
$1 = x$
$x = 1$