# How do you solve 4 (5x + 7) - 3x= 3(4x - 9)?

Mar 5, 2017

See the entire solution process below:

#### Explanation:

First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside of the parenthesis:

$\textcolor{red}{4} \left(5 x + 7\right) - 3 x = \textcolor{b l u e}{3} \left(4 x - 9\right)$

$\left(\textcolor{red}{4} \times 5 x\right) + \left(\textcolor{red}{4} \times 7\right) - 3 x = \left(\textcolor{b l u e}{3} \times 4 x\right) - \left(\textcolor{b l u e}{3} \times 9\right)$

$20 x + 28 - 3 x = 12 x - 27$

$20 x - 3 x + 28 = 12 x - 27$

$17 x + 28 = 12 x - 27$

Next, subtract $\textcolor{red}{28}$ and $\textcolor{b l u e}{12 x}$ from each side of the equation to isolate the $x$ terms while keeping the equation balanced:

$17 x + 28 - \textcolor{red}{28} - \textcolor{b l u e}{12 x} = 12 x - 27 - \textcolor{red}{28} - \textcolor{b l u e}{12 x}$

$17 x - \textcolor{b l u e}{12 x} + 28 - \textcolor{red}{28} = 12 x - \textcolor{b l u e}{12 x} - 27 - \textcolor{red}{28}$

$5 x + 0 = 0 - 55$

$5 x = - 55$

Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $x$ while keeping the equation balanced:

$\frac{5 x}{\textcolor{red}{5}} = - \frac{55}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = - 11$

$x = - 11$