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

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

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Answer 1 · 2015-03-25T13:59:04

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

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

It looks like this:

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

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

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

$\frac{- x}{- 1} = \frac{- 1}{- 1}$ $(-x)/(-1)=(-1)/(-1)$

$x = 1$ $x=1$

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

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

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

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

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

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