# How do you solve 1/2x+3/4=1/6 by clearing the fractions?

Apr 5, 2017

$x = - \frac{7}{6}$

#### Explanation:

First subtract $\frac{3}{4}$ from both sides giving you,

$\frac{x}{2} = \frac{1}{6} - \frac{3}{4}$

Find common denominator,

$\frac{x}{2} = \frac{2}{12} - \frac{9}{12}$

Simplify,

$\frac{x}{2} = - \frac{7}{12}$

Multiply both sides by 2,

$x = 2 \cdot \left(- \frac{7}{12}\right) = - \frac{14}{12}$

Reduce for the final answer of,

$x = - \frac{7}{6}$

Apr 5, 2017

Multiply all the terms by the least common denominator.

#### Explanation:

The LCM of 2,4,and 6 is 12

Multiplying all of the terms by 12 results in

$12 \times 1 \frac{x}{2} + 12 \times \frac{3}{4} = 12 \times \frac{1}{6}$ This gives
h
$6 x + 9 = 2$ subtract 9 from both sides gives

$6 x + 9 - 9 = 2 - 9$ which results in

$6 x = - 7$ divide both sides by 6

$6 \frac{x}{6} = - \frac{7}{6}$

$x = - \frac{7}{6}$