# How do you solve and check your solution given x-2/5=-8/15?

Feb 19, 2017

See the entire solution and validation process below:

#### Explanation:

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

$\textcolor{red}{15} \left(x - \frac{2}{5}\right) = \textcolor{red}{15} \times - \frac{8}{15}$

$\left(\textcolor{red}{15} \times x\right) - \left(\textcolor{red}{15} \times \frac{2}{5}\right) = \cancel{\textcolor{red}{15}} \times - \frac{8}{\textcolor{red}{\cancel{\textcolor{b l a c k}{15}}}}$

$15 x - \left(\cancel{\textcolor{red}{15}} 3 \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}\right) = - 8$

$15 x - 6 = - 8$

Next, add $\textcolor{red}{6}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$15 x - 6 + \textcolor{red}{6} = - 8 + \textcolor{red}{6}$

$15 x - 0 = - 2$

$15 x = - 2$

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

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

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

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

To validate the solution we need to substitute $\textcolor{red}{- \frac{2}{15}}$ back into the original equation for $\textcolor{red}{x}$ and calculate the left side of the equation to ensure it equals $- \frac{8}{15}$:

$\textcolor{red}{x} - \frac{2}{5} = - \frac{8}{15}$ becomes:

$\textcolor{red}{- \frac{2}{15}} - \frac{2}{5} = - \frac{8}{15}$

$\textcolor{red}{- \frac{2}{15}} - \left(\frac{3}{3} \times \frac{2}{5}\right) = - \frac{8}{15}$

$\textcolor{red}{- \frac{2}{15}} - \frac{6}{15} = - \frac{8}{15}$

$- \frac{8}{15} = - \frac{8}{15}$ therefore we have checked our solution.