# How do you solve x-2/3=-4/5?

Feb 7, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{15}$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{15} \left(x - \frac{2}{3}\right) = \textcolor{red}{15} \times - \frac{4}{5}$

$\left(\textcolor{red}{15} \times x\right) - \left(\textcolor{red}{15} \times \frac{2}{3}\right) = \cancel{\textcolor{red}{15}} 3 \times - \frac{4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}$

$15 x - \left(\cancel{\textcolor{red}{15}} 5 \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}\right) = - 12$

$15 x - 10 = - 12$

Next, add $\textcolor{red}{10}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$15 x - 10 + \textcolor{red}{10} = - 12 + \textcolor{red}{10}$

$15 x - 0 = - 2$

$15 x = - 2$

Now, divide each side of the equation by $\textcolor{red}{15}$ to solve for $x$ while keeping the equation balanced:

$\frac{15 x}{\textcolor{red}{15}} = - \frac{2}{\textcolor{red}{15}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{15}}} x}{\cancel{\textcolor{red}{15}}} = - \frac{2}{15}$

$x = - \frac{2}{15}$