# How do you solve and check your solution given m+7/12=-5/18?

Jun 17, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{\frac{7}{12}}$ from each side of the equation to solve for $m$:

$m + \frac{7}{12} - \textcolor{red}{\frac{7}{12}} = - \frac{5}{18} - \textcolor{red}{\frac{7}{12}}$

$m + 0 = - \frac{5}{18} - \textcolor{red}{\frac{7}{12}}$

$m = - \frac{5}{18} - \textcolor{red}{\frac{7}{12}}$

To add/subtract the two factions we need to get them over a common denominator:

$m = - \left(\frac{2}{2} \times \frac{5}{18}\right) - \left(\frac{3}{3} \times \textcolor{red}{\frac{7}{12}}\right)$

$m = - \frac{10}{36} - \frac{21}{36}$

$m = - \frac{31}{36}$

To check the solution, substitute $- \frac{31}{36}$ for $m$ in the original equation and calculate the result for both sides of the equation to ensure they are equal:

$m + \frac{7}{12} = - \frac{5}{18}$ becomes:

$- \frac{31}{36} + \frac{7}{12} = - \frac{5}{18}$

$- \frac{31}{36} + \left(\frac{3}{3} \times \frac{7}{12}\right) = - \frac{5}{18}$

$- \frac{31}{36} + \frac{21}{36} = - \frac{5}{18}$

$- \frac{10}{36} = - \frac{5}{18}$

$- \frac{2 \times 5}{2 \times 18} = - \frac{5}{18}$

$- \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 18} = - \frac{5}{18}$

$- \frac{5}{18} = - \frac{5}{18}$

Because both sides of the equation are equal the result checks out.