# How do you solve 31=-(1+6p)+4(p+6) using the distributive property?

May 27, 2017

$p = - 4$

#### Explanation:

$31 = \textcolor{red}{- 1} \left(1 + 6 p\right) \textcolor{red}{+ 4} \left(p + 6\right)$

$\text{multiplying out the brackets (distributive property ) gives}$

$31 = - 1 - 6 p + 4 p + 24$

$31 = 23 - 2 p \leftarrow \text{ simplifying right side}$

$\text{subtract 23 from both sides}$

$31 - 23 = \cancel{23} \cancel{- 23} - 2 p$

$\Rightarrow - 2 p = 8 \leftarrow \text{ reversing the equation}$

$\text{divide both sides by - 2}$

$\frac{\cancel{- 2} \textcolor{w h i t e}{x} p}{\cancel{- 2}} = \frac{8}{- 2}$

$\Rightarrow p = - 4$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the right side of the equation and if equal to the left side then it is the solution.

$- \left(1 - 24\right) + 4 \left(- 4 + 6\right) = 23 + 8 = 31 = \text{left side}$

$\Rightarrow p = - 4 \text{ is the solution}$