# How do you solve 5/12g+2/3=1/8?

Mar 12, 2017

See the entire solution process below:

#### Explanation:

First, multiply both sides of the equation by $\textcolor{red}{24}$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{24} \left(\frac{5}{12} g + \frac{2}{3}\right) = \textcolor{red}{24} \times \frac{1}{8}$

$\left(\textcolor{red}{24} \times \frac{5}{12} g\right) + \left(\textcolor{red}{24} \times \frac{2}{3}\right) = \cancel{\textcolor{red}{24}} 3 \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}}$

$\left(\cancel{\textcolor{red}{24}} 2 \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}}} g\right) + \left(\cancel{\textcolor{red}{24}} 8 \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}\right) = 3$

$10 g + 16 = 3$

Next, subtract $\textcolor{red}{16}$ from each side of the equation to isolate the $g$ term while keeping the equation balanced:

$10 g + 16 - \textcolor{red}{16} = 3 - \textcolor{red}{16}$

$10 g + 0 = - 13$

$10 g = - 13$

Now, divide each side of the equation by $\textcolor{red}{10}$ to solve for $g$ while keeping the equation balanced:

$\frac{10 g}{\textcolor{red}{10}} = - \frac{13}{\textcolor{red}{10}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} g}{\cancel{\textcolor{red}{10}}} = - \frac{13}{10}$

$g = - \frac{13}{10}$