# How do you solve 1/2x+5/6=7/12?

Apr 12, 2017

If there are fractions in an equation, you can get rid of the denominators by multiplying though by the LCM of the denominators:

$\frac{1}{2} x + \frac{5}{6} = \frac{7}{12} \text{ } \leftarrow L C M = 12$

$\frac{\textcolor{red}{{\cancel{12}}^{6} \times 1 x}}{\cancel{2}} + \frac{\textcolor{red}{{\cancel{12}}^{2} \times 5}}{\cancel{6}} = \frac{\textcolor{red}{\cancel{12} \times 7}}{\cancel{12}} \text{ } \leftarrow$ cancel denominators

$6 x + 10 = 7$

$\text{ } 6 x = 7 - 10$

$\text{ } 6 x = - 3$

$\text{ } x = - \frac{1}{2}$