How do you solve -3p + 8= 6- ( 12p + 5)?

Apr 1, 2017

See the entire solution process below:

Explanation:

First, remove the terms from parenthesis on the right side of the equation, group and combine like terms:

$- 3 p + 8 = 6 - \left(12 p + 5\right)$

$- 3 p + 8 = 6 - 12 p - 5$

$- 3 p + 8 = 6 - 5 - 12 p$

$- 3 p + 8 = 1 - 12 p$

Next, subtract $\textcolor{red}{8}$ and add $\textcolor{b l u e}{12 p}$ to each side of the equation to isolate the $p$ term while keeping the equation balanced:

$- 3 p + 8 - \textcolor{red}{8} + \textcolor{b l u e}{12 p} = 1 - 12 p - \textcolor{red}{8} + \textcolor{b l u e}{12 p}$

$- 3 p + \textcolor{b l u e}{12 p} + 8 - \textcolor{red}{8} = 1 - \textcolor{red}{8} - 12 p + \textcolor{b l u e}{12 p}$

$\left(- 3 + \textcolor{b l u e}{12}\right) p + 0 = - 7 - 0$

$9 p = - 7$

Now, divide each side of the equation by $\textcolor{red}{9}$ to solve for $p$ while keeping the equation balanced:

$\frac{9 p}{\textcolor{red}{9}} = - \frac{7}{\textcolor{red}{9}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} p}{\cancel{\textcolor{red}{9}}} = - \frac{7}{9}$

$p = - \frac{7}{9}$