# How do you solve 2( 2- 2x ) = 4- 8( 1- x ) ?

Jun 5, 2017

#### Answer:

$x = \frac{2}{3} \mathmr{and} 0.66 \dot{6}$

#### Explanation:

$2 \left(2 - 2 x\right) = 4 - 8 \left(1 - x\right)$

We can expand the brackets.

$4 - 4 x = 4 - 8 \left(1 - x\right)$

$4 - 4 x = 4 - 8 - - 8 x$

$4 - 4 x = 4 - 8 + 8 x$

$4 - 4 x = - 4 + 8 x$

We can Move the $4$ over to the right side.

$- 4 x = - 4 + 8 x - 4$

We can Move the $- 8 x$ over to the left side.

$- 4 x - 8 x = - 4 - 4$

we can solve these equations.

$- 12 x = - 4 - 4$

$- 12 x = - 8$

We can isolate $x$ by moving $- 12$ to the other side of the equation.

x = -8 ÷ -12

color(blue)(x = 2/3 or 0.66dot6#

We can prove our answer by substituting $\frac{2}{3}$ for $x$ in the equation and see if we are correct.

$2 \left(2 - 2 x\right) = 4 - 8 \left(1 - x\right)$

$2 \left(2 - 2 \times \frac{2}{3}\right) = 4 - 8 \left(1 - \frac{2}{3}\right)$

Now we can use $\text{BODMAS}$ or $\text{PEMDAS}$ to solve the equation.

$\text{BOMDAS}$ = Brackets, Order (Power), Multiplication, Division, Addition and Subtraction

$\text{PEMDAS}$ = Power, Exponents, Multiplication, Division, Addition and Subtraction

$2 \left(2 - 2 \times \frac{2}{3}\right) = 4 - 8 \left(1 - \frac{2}{3}\right)$

$2 \left(2 - 1 \frac{1}{3}\right) = 4 - 8 \left(1 - \frac{2}{3}\right)$

$2 \left(2 - 1 \frac{1}{3}\right) = 4 - 8 \left(\frac{1}{3}\right)$

$2 \times \frac{2}{3} = 4 - 8 \left(\frac{1}{3}\right)$

$2 \times \frac{2}{3} = 4 - 2 \frac{2}{3}$

$2 \times \frac{2}{3} = 1 \frac{1}{3}$

$1 \frac{1}{3} = 1 \frac{1}{3}$