# How do you solve -4(3x-2)=-32 using the distributive property?

May 28, 2018

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

#### Explanation:

We will use the distributive property (shown below) to simplify $- 4 \left(3 x - 2\right)$:

Following this image, we know that:
$\textcolor{b l u e}{- 4 \left(3 x - 2\right) = \left(- 4 \cdot 3 x\right) + \left(- 4 \cdot - 2\right) = - 12 x + 8}$

Put that back into the equation:
$- 12 x + 8 = - 32$

Now subtract $\textcolor{b l u e}{8}$ from both sides of the equation:
$- 12 x + 8 \quad \textcolor{b l u e}{- \quad 8} = - 32 \quad \textcolor{b l u e}{- \quad 8}$

$- 12 x = - 40$

Next, divide both sides by $\textcolor{b l u e}{- 12}$:
$\frac{- 12 x}{\textcolor{b l u e}{- 12}} = \frac{- 40}{\textcolor{b l u e}{- 12}}$

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

Hope this helps!