# How do you solve 3/8x+5/6=5/4x+2/3 by clearing the fractions?

Mar 12, 2017

Multiply both sides of the equation by a common factor such as $24.$

#### Explanation:

Multiply both sides of the equation by a common factor such as $24$:
$24 \cdot \left(\frac{3}{8} x + \frac{5}{6}\right) = 24 \cdot \left(\frac{5}{4} x + \frac{2}{3}\right)$

Simplify by dividing first, then multiplying:
$\frac{24 \cdot 3}{8} x + \frac{24 \cdot 5}{6} = \frac{24 \cdot 5}{4} x + \frac{24 \cdot 2}{3}$

$3 \cdot 3 x + 4 \cdot 5 = 6 \cdot 5 x + 8 \cdot 2$

$9 x + 20 = 30 x + 16$

$9 x - 30 x = 16 - 20$
$- 21 x = - 4$
Divide by $- 21$ to isolate the variable $x$: $x = \frac{4}{21}$