# How do you solve and check your solution given 2/3p=-22?

Feb 27, 2017

See the entire solution and verification process below:

#### Explanation:

First, multiply each side of the equation by $\frac{\textcolor{red}{3}}{\textcolor{b l u e}{2}}$ to solve for $p$ while keeping the equation balanced:

$\frac{\textcolor{red}{3}}{\textcolor{b l u e}{2}} \times \frac{2}{3} p = \frac{\textcolor{red}{3}}{\textcolor{b l u e}{2}} \times - 22$

$\frac{\cancel{\textcolor{red}{3}}}{\cancel{\textcolor{b l u e}{2}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{2}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} p = - \frac{66}{\textcolor{b l u e}{2}}$

$p = - 33$

To verify the solution, substitute $\textcolor{red}{- 33}$ for $\textcolor{red}{p}$ in the original equation and calculate the left side of the equation to ensure it equals $- 22$:

$\frac{2}{3} \textcolor{red}{p} = - 22$ becomes:

$\frac{2}{3} \times \textcolor{red}{- 33} = - 22$

$- \frac{66}{3} = - 22$

$- 22 = - 22$

Because both sides of the equation calculate to $- 22$ the solution for $p$ is verified to be $- 33$.