# How do you solve and check your solutions to -2/7v=16?

Aug 21, 2017

See a solution process below:

#### Explanation:

Multiply each side of the equation by $\frac{\textcolor{red}{7}}{\textcolor{b l u e}{- 2}}$ to solve for $v$ while keeping the equation balanced:

$\frac{\textcolor{red}{7}}{\textcolor{b l u e}{- 2}} \times \frac{- 2}{7} v = \frac{\textcolor{red}{7}}{\textcolor{b l u e}{- 2}} \times 16$

$\frac{\cancel{\textcolor{red}{7}}}{\cancel{\textcolor{b l u e}{- 2}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 2}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}} v = \frac{\textcolor{red}{7}}{- \cancel{\textcolor{b l u e}{2}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{16}}} 8$

$v = \frac{56}{-} 1$

$v = - 56$

To check the solution, substitute $- 56$ for $v$ in the original equation and ensure the left side of the equation calculates to $16$:

$- \frac{2}{7} v = 16$ becomes:

$- \frac{2}{7} \cdot - 56 = 16$

$- \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}} \cdot - 8 \textcolor{red}{\cancel{\textcolor{b l a c k}{56}}} = 16$

$- 2 \cdot - 8 = 16$

$16 = 16$