# How do you solve  2/3x=6?

May 3, 2018

Multiply both sides by the reciprocal of the fraction on the left-hand side to get $x = 9$

#### Explanation:

We will multiply both sides by the reciprocal of the fraction on the left-hand side. This will eliminate $x$'s coefficient and give us our answer:

$\cancel{\frac{2}{3}} x \cancel{\textcolor{red}{\times \frac{3}{2}}} = 6 \textcolor{red}{\times \frac{3}{2}}$

$x = 6 \times \frac{3}{2}$

$x = \frac{6}{1} \times \frac{3}{2}$

$x = \frac{18}{2}$

$\textcolor{g r e e n}{x = 9}$

May 3, 2018

$x = 9$

#### Explanation:

$\frac{2}{3} x = 6 \rightarrow$ Divide both sides by $\frac{2}{3}$

$x = \frac{6}{\frac{2}{3}}$

$x = 6 \cdot \frac{3}{2}$

$6 \cdot \frac{3}{2} = \frac{6}{1} \cdot \frac{3}{2} = \frac{3 \cancel{6}}{1} \cdot \frac{3}{\cancel{2}} = \frac{9}{1} = 9$

$x = 9$