# How do you solve 6=2(-4+2x)-2(1+6x) using the distributive property?

Sep 30, 2017

$x = - 2$

#### Explanation:

$\text{distribute the brackets using the distributive property}$

•color(white)(x)a(b+c)=ab+ac

$\Rightarrow 6 = - 8 + 4 x - 2 - 12 x$

$\Rightarrow 6 = - 10 - 8 x$

$\text{add 10 to both sides}$

$6 + 10 = \cancel{- 10} \cancel{+ 10} - 8 x$

$\Rightarrow 16 = - 8 x$

$\text{divide both sides by } - 8$

$\frac{16}{- 8} = \frac{\cancel{- 8} x}{\cancel{- 8}}$

$\Rightarrow x = - 2$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the right side of the equation and if equal to the left side then it is the solution.

$2 \left(- 4 - 4\right) - 2 \left(1 - 12\right) = \left(2 \times - 8\right) - \left(2 \times - 11\right) = - 16 + 22 = 6$

$\Rightarrow x = - 2 \text{ is the solution}$

Sep 30, 2017

$x = - 2$

#### Explanation:

Question : $6 = 2 \left(- 4 + 2 x\right) - 2 \left(1 + 6 x\right)$

Distributive property :

$a \left(b - c\right) = a b - a c$

Let us apply the distributive property :

$2 \left(- 4 + 2 x\right)$ will give us $\left(2 \setminus \times - 4\right) + \left(2 \setminus \times 2 x\right)$

and

$2 \left(1 + 6 x\right)$ will give us $\left(2 \setminus \times 1\right) + \left(2 \setminus \times 6 x\right)$

So, by the distributive property,

$\left[2 \left(- 4 + 2 x\right)\right] - \left[2 \left(1 + 6 x\right)\right] = 6$

can also be written as :

$\left[\left(2 \setminus \times - 4\right) + \left(2 \setminus \times 2 x\right)\right] - \left[\left(2 \setminus \times 1\right) + \left(2 \setminus \times 6 x\right)\right] = 6$

Multiplication :

$\left[\left(- 8\right) + \left(4 x\right)\right] - \left[\left(2\right) + \left(12 x\right)\right] = 6$

Removing the Parenthesis :

$- 8 + 4 x - 2 - 12 x = 6$

Grouping the like terms :

$\left(- 8 - 2\right) + \left(4 x - 12 x\right) = 6$

$- 10 - 8 x = 6$

Transposition :

$- 8 x = 6 + 10$

$- 8 x = 16$

$- x = \frac{16}{8}$

$- x = 2$

$x = - 2$