# How do you solve 4x-2(1-x)=2(3x-2)?

Jun 23, 2016

You cannot, it is a contradiction.

#### Explanation:

Two ways:

1.
$4 x - 2 \left(1 - x\right) = 2 \left(3 x - 2\right)$ factor out 2

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

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

$3 x - 1 = 3 x - 2$ + 1 to both sides (by this point we can see it is a contradiction)

$3 x = 3 x - 1$ divide by 3

 x ≠ x - (1/3)  impossible / false statment

2.
$4 x - 2 \left(1 - x\right) = 2 \left(3 x - 2\right)$ expand brackets

$4 x - 2 + 2 x = 6 x - 4$ combine like terms (simplify)

$6 x - 2 = 6 x - 4$ divide by 2 (by this point we can see it is a contradiction)

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

$3 x = 3 x - 1$ divide by 3

 x ≠ x - (1/3)  impossible / false statment

In both ways we see a statement which is false . You can never have $x = x - \left(\frac{1}{3}\right)$ or any similar statement - it's like saying 1 = 1 - (1/3). It is just not true. Therefore the original statement is a contradiction and cannot be solved.