# How do you solve x+2/5=-3/2 by clearing the fractions?

May 2, 2017

$\textcolor{g r e e n}{x = - \frac{19}{10}}$
$\textcolor{w h i t e}{\text{XXX}}$see below for solution method by "clearing the fractions"

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{x + \frac{2}{5}} = \textcolor{b l u e}{- \frac{3}{2}}$

We can clear the fractions by multiplying both sides by the $\textcolor{red}{L C M}$ (Least Common Multiple) of all denominators appearing in the equation.

The denominators that we have in the given equation are $\textcolor{b l u e}{2}$ and $\textcolor{b l u e}{5}$;
their color(red)(LCM) is $\textcolor{red}{10}$;
so we will multiply both sides by $\textcolor{red}{10}$

$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{10} \times \left(\textcolor{b l u e}{x + \frac{2}{5}}\right) = \textcolor{red}{10} \times \left(\textcolor{b l u e}{- \frac{3}{2}}\right)$

Simplifying
$\textcolor{w h i t e}{\text{XXX}} 10 x + 4 = - 15$

$\textcolor{w h i t e}{\text{XXX}} 10 x = - 19$

$\textcolor{w h i t e}{\text{XXX}} x = - \frac{19}{10}$