# How do you solve 3/11x+1/2=3/4?

May 23, 2017

$x = \frac{11}{12}$

#### Explanation:

One strategy for solving this problem is to eliminate the fractions first. In order to get rid of the fractions, you would have to multiply both sides of the equation by a number which evenly divides into all of the denominators, namely, $11$, $2$, and $4$.

Because $44$ divides evenly into $11$, $2$, and $4$, lets multiply both sides by $44$:

$44 \times \left(\frac{3}{11} x + \frac{1}{2}\right) = 44 \times \left(\frac{3}{4}\right)$

On the left, distribute the $44$ to both terms inside the parenthesis:
$44 \times \frac{3}{11} x + 44 \times \frac{1}{2} = 44 \times \frac{3}{4}$

Next, simplify by reducing these fractions
$4 \times 3 x + 22 \times 1 = 11 \times 3$

$12 x + 22 = 33$
Subtract $22$ from both sides
$12 x = 11$
Divide both sides by $12$
$x = \frac{11}{12}$