# How do you solve 5/6(12p+4)=-13p+4?

Jan 26, 2017

See the entire solution process below:

#### Explanation:

First, multiply both sides of the equation by $\textcolor{red}{6}$ to eliminate the fraction and keep the equation balanced:

$\textcolor{red}{6} \times \frac{5}{6} \left(12 p + 4\right) = \textcolor{red}{6} \left(- 13 p + 4\right)$

$\cancel{\textcolor{red}{6}} \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}} \left(12 p + 4\right) = \textcolor{red}{6} \left(- 13 p + 4\right)$

$5 \left(12 p + 4\right) = \textcolor{red}{6} \left(- 13 p + 4\right)$

$60 p + 20 = - 78 p + 24$

Next add $\textcolor{red}{78 p}$ and subtract $\textcolor{b l u e}{20}$ from each side of the equation to isolate the $p$ terms while keeping the equation balanced:

$60 p + 20 + \textcolor{red}{78 p} - \textcolor{b l u e}{20} = - 78 p + 24 + \textcolor{red}{78 p} - \textcolor{b l u e}{20}$

$60 p + \textcolor{red}{78 p} + 20 - \textcolor{b l u e}{20} = - 78 p + \textcolor{red}{78 p} + 24 - \textcolor{b l u e}{20}$

$138 p + 0 = 0 + 4$

$138 p = 4$

Now, divide each side of the equation by $\textcolor{red}{138}$ to solve for $p$ while keeping the equation balanced:

$\frac{138 p}{\textcolor{red}{138}} = \frac{4}{\textcolor{red}{138}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{138}}} p}{\cancel{\textcolor{red}{138}}} = \frac{2}{69}$

$p = \frac{2}{69}$