# How do you solve 5/7x-3/14=-3/8x+3/4?

May 11, 2018

$x = \frac{54}{61}$

#### Explanation:

The easiest way to solve this is to get rid of the denominators first.
The least common multiple of 7, 14, 8 and 4 would be $7 \cdot 8 = 4 \cdot 14 = 56$.

Therefore, multiply both sides with 56=4*14:
$\left(\frac{5}{7} x - \frac{3}{14}\right) \cdot 4 \cdot 14 = \left(- \frac{3}{8} x + \frac{3}{4}\right) \cdot 8 \cdot 7$

Simplifying we get:
$5 \cdot 8 x - 3 \cdot 4 = - 3 \cdot 7 x + 3 \cdot 14$
or: $40 x - 12 = - 21 x + 42$

Adding $21 x + 12$ to both sides to get the x terms to the left and the constants to the right, we get:
$40 x + 21 x = 42 + 12$
$61 x = 54$
Dividing on 61 on both sides we get
$x = \frac{54}{61}$

As $61$ is a prime number, we cannot simplify this more .