# How do you solve 13- 3p = - 5( 3+ 2p )?

Jun 29, 2018

$p = - 4$

#### Explanation:

$13 - 3 p = - 5 \left(3 + 2 p\right)$

First, use the distributive property (shown below) to simplify $- 5 \left(3 + 2 p\right)$:

Following this image, we know that:
$\textcolor{b l u e}{- 5 \left(3 + 2 p\right) = \left(- 5 \cdot 3\right) + \left(- 5 \cdot 2 p\right) = - 15 - 10 p}$

Put it back into the equation:
$13 - 3 p = - 15 - 10 p$

Add $\textcolor{b l u e}{10 p}$ on both sides of the equation:
$13 - 3 p \quad \textcolor{b l u e}{+ \quad 10 p} = - 15 - 10 p \quad \textcolor{b l u e}{+ \quad 10 p}$

$13 + 7 p = - 15$

Subtract $\textcolor{b l u e}{13}$ from both sides:
$13 + 7 p \quad \textcolor{b l u e}{- \quad 13} = - 15 \quad \textcolor{b l u e}{- \quad 13}$

$7 p = - 28$

Divide both sides $\textcolor{b l u e}{7}$:
$\frac{7 p}{\textcolor{b l u e}{7}} = \frac{- 28}{\textcolor{b l u e}{7}}$

Therefore,
$p = - 4$

Hope this helps!

Aug 5, 2018

$p = - 4$

#### Explanation:

We can distribute the $- 5$ on the right to get

$- 3 p + 13 = - 15 - 10 p$

We can start by adding $10 p$ to both sides to get

$7 p + 13 = - 15$

Next, to get our constants on one side, we can subtract $13$ from both sides. We now have

$7 p = - 28$

To completely isolate the $p$ term, we can divide both sides by $7$. We get

$p = - 4$

Hope this helps!