# How do you solve 7x + 3( 2x - 6) = 3x + 8?

May 3, 2018

$x = \frac{13}{5}$

#### Explanation:

$7 x + 3 \left(2 x - 6\right) = 3 x + 8$

First, distribute $3 \left(2 x - 6\right)$ using the distributive property:

Following this image, we know that the expression will simplify to:
$\left(3 \cdot 2 x\right) + \left(3 \cdot - 6\right)$

$\implies 6 x - 18$

Let's put this back into the equation:
$7 x + 6 x - 18 = 3 x + 8$

Now combine like terms on the left side of the equation:
$13 x - 18 = 3 x + 8$

Now subtract $\textcolor{b l u e}{3 x}$ on both sides of the equation:
$13 x - 18 \quad \textcolor{b l u e}{- \quad 3 x} = 3 x + 8 \quad \textcolor{b l u e}{- \quad 3 x}$

$10 x - 18 = 8$

Add $\textcolor{b l u e}{18}$ to both sides of the equation:
$10 x - 18 \quad \textcolor{b l u e}{+ \quad 18} = 8 \quad \textcolor{b l u e}{+ \quad 18}$

$10 x = 26$

Divide both sides by $\textcolor{b l u e}{10}$:
$\frac{10 x}{\textcolor{b l u e}{10}} = \frac{26}{\textcolor{b l u e}{10}}$:
$x = \frac{26}{10}$

Divide numerator and denominator by $\textcolor{b l u e}{2}$:
$x = \frac{26}{10} \textcolor{b l u e}{\div \frac{2}{2}}$

$x = \frac{13}{5}$