# How do you solve and check your solution given -6=3/5a?

Jun 9, 2017

See a solution process below:

#### Explanation:

Multiply each side of the equation by $\frac{\textcolor{red}{5}}{\textcolor{b l u e}{3}}$ to solve for $a$ while keeping the equation balanced:

$\frac{\textcolor{red}{5}}{\textcolor{b l u e}{3}} \times - 6 = \frac{\textcolor{red}{5}}{\textcolor{b l u e}{3}} \times \frac{3}{5} a$

$- \frac{30}{\textcolor{b l u e}{3}} = \frac{\cancel{\textcolor{red}{5}}}{\cancel{\textcolor{b l u e}{3}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} a$

$- 10 = a$

$a = - 10$

To check the solution substitute $\textcolor{red}{- 10}$ for $\textcolor{red}{a}$ in the original equation and calculate the result on the right side of the equation to ensure it equals $- 6$

$- 6 = \frac{3}{5} \textcolor{red}{a}$ becomes:

$- 6 = \frac{3}{5} \times \textcolor{red}{- 10}$

$- 6 = \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} \times \cancel{\textcolor{red}{- 10}} - 2$

$- 6 = 3 \times - 2$

$- 6 = - 6$

Therefore the solution is correct.