# How do you solve 1/2 (x-3) = 1/3 (2x+1)?

Jun 1, 2015

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

We are going to put it all on six by multiplying both denominators and numerators

$\frac{3 x}{6} - \frac{9}{6} = \frac{4 x}{6} + \frac{2}{6}$

We substract $\frac{2}{6}$ on both sides

$\frac{3 x}{6} - \frac{9}{6} - \frac{2}{6} = \frac{4 x}{6}$

$\frac{3 x}{6} - \frac{11}{6} = \frac{4 x}{6}$

We substract $\frac{3 x}{6}$ on both side

$- \frac{11}{6} = \frac{4 x}{6} - \frac{3 x}{6}$

$- \frac{11}{6} = \frac{x}{6}$

We multiply both side by six to get $x$

$x = - 11$