# How do you solve 2 / 3 (x − 2) = 4x  and find any extraneous solutions?

Apr 22, 2017

$x = - \frac{2}{5}$

#### Explanation:

Multiply both sides of the equation by $\frac{3}{2}$

$\frac{\cancel{3}}{\cancel{2}} \times \frac{\cancel{2}}{\cancel{3}} \left(x - 2\right) = \frac{3}{\cancel{2}} \times {\cancel{4}}^{2} x$

$x - 2 = 6 x$

$- 2 = 5 x \text{ } \leftarrow \div 5$

$- \frac{2}{5} = x$

$x$ is not in the denominator and there are no restrictions on $x$, therefore there are no extraneous solutions.