# How do you solve and check your solutions to -108=9j?

Feb 4, 2017

See the entire solution and validation process below:

#### Explanation:

$\textcolor{red}{S o l u t i o n}$ $\textcolor{red}{P r o c e s s}$

Divide each side of the equation by $\textcolor{red}{9}$ to solve for $j$ while keeping the equation balanced:

$\frac{- 108}{\textcolor{red}{9}} = \frac{9 j}{\textcolor{red}{9}}$

$- 12 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} j}{\cancel{\textcolor{red}{9}}}$

$- 12 = j$

$j = - 12$

$\textcolor{red}{V a l i \mathrm{da} t i o n}$ $\textcolor{red}{P r o c e s s}$

To validate this we need to substitute $\textcolor{red}{- 12}$ for $\textcolor{red}{j}$ in the original equation and calculate the right side of the equation to ensure it equals $- 108$:

$- 108 = 9 \textcolor{red}{j}$ becomes:

$- 108 = 9 \times \textcolor{red}{- 12}$

$- 108 = - 108$

The two sides of the equation are equal therefore the solution to this problem is $j = - 12$