# How do you solve 4( 4x + 3) - 12= 5- 6( 5x + 2)?

May 11, 2018

$x = - \frac{7}{46}$

#### Explanation:

First, use the distributive property to simplify $\textcolor{b l u e}{4 \left(4 x + 3\right)}$ and $\textcolor{b l u e}{- 6 \left(5 x + 2\right)}$:

Following this image, we know that:
$\textcolor{b l u e}{4 \left(4 x + 3\right) = \left(4 \cdot 4 x\right) + \left(4 \cdot 3\right) = 16 x + 12}$

and

$\textcolor{b l u e}{- 6 \left(5 x + 2\right) = \left(- 6 \cdot 5 x\right) - \left(6 \cdot 2\right) = - 30 x - 12}$

Now let's put them back into the equation:
$16 x + 12 - 12 = 5 - 30 x - 12$

Simplify:
$16 x = - 7 - 30 x$

Add $\textcolor{b l u e}{30 x}$ to both sides of the equation:
$16 x \quad \textcolor{b l u e}{+ \quad 30 x} = - 7 - 30 x \quad \textcolor{b l u e}{+ \quad 30 x}$

$46 x = - 7$

Divide both sides by $\textcolor{b l u e}{46}$:
$\frac{46 x}{\textcolor{b l u e}{46}} = - \frac{7}{\textcolor{b l u e}{46}}$

Therefore,
$x = - \frac{7}{46}$

Hope this helps!