# How do you solve 9p + 5- p = - 7?

Apr 9, 2017

See the entire solution process below:

#### Explanation:

First, group and combine like terms on the left side of the equation:

$9 p + 5 - p = - 7$

$9 p - p + 5 = - 7$

$9 p - 1 p + 5 = - 7$

$\left(9 - 1\right) p + 5 = - 7$

$8 p + 5 = - 7$

Next, subtract $\textcolor{red}{5}$ from each side of the equation to isolate the $p$ term while keeping the equation balanced:

$8 p + 5 - \textcolor{red}{5} = - 7 - \textcolor{red}{5}$

$8 p + 0 = - 12$

$8 p = - 12$

Now, divide each side of the equation by $\textcolor{red}{8}$ to solve for $p$ while keeping the equation balanced:

$\frac{8 p}{\textcolor{red}{8}} = - \frac{12}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} p}{\cancel{\textcolor{red}{8}}} = \frac{4 \times - 3}{\textcolor{red}{4 \times 2}}$

$p = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times - 3}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{4}}} \times 2}}$

$p = - \frac{3}{2}$

Apr 9, 2017

$p = - 1.5$

#### Explanation:

Your main goals are to get $p$ alone, and all like terms on one side!

First, subtract $5$ so you can put the like terms together ($9 p$ and $- p$). Remember, what you do to one side must be done to the other. now your equation is

$9 p - p = - 7 - 5$

Now solve for the like terms ($9 p$ and $- p$ and $- 7$ and $- 5$), which gives you

$8 p = - 12$

To get $p$ alone, divide both sides by $8$ (what you do to one side must be done to the other). you now have your solution!

$p = - 1.5$