# How do you solve x/6+3/2=(2x)/3-1 and check for extraneous solutions?

Nov 23, 2016

$x = 5$

#### Explanation:

$\frac{x}{6} + \frac{3}{2} = \frac{2 x}{3} - 1$

One way to do it is to write everything with the same denominator:
$\frac{x}{6} + \frac{9}{6} = \frac{4 x}{6} - \frac{6}{6}$
x+9=4x-6

Subtract 4x +9 from each side:
$- 3 x = - 15$

Divide each side by -3:
$x = 5$