# How do you solve 5/8x=-2/3 by clearing the fractions?

Feb 12, 2017

First, we need to multiply each side of the equation by the common denominator of the two fractions. The common denominator is $8 \times 3 = \textcolor{red}{24}$

$\frac{5}{8} x \times \textcolor{red}{24} = - \frac{2}{3} \times \textcolor{red}{24}$

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

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

$5 x \times 3 = - 2 \times 8$

$15 x = - 16$

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

$\frac{15 x}{\textcolor{red}{15}} = - \frac{16}{\textcolor{red}{15}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{15}}} x}{\cancel{\textcolor{red}{15}}} = - \frac{16}{15}$

$x = - \frac{16}{15}$