# How do you solve (4x)/15-5/6=2/3 by clearing the fractions?

May 7, 2017

$x = 5 \frac{5}{8} = 5.625$

#### Explanation:

When you have an equation with fractions, you can get rid of the denominators by multiplying each fraction by the LCM to the denominators can cancel.

$\frac{4 x}{15} - \frac{5}{6} = \frac{2}{3} \text{ } \leftarrow L C M = 30$

$\frac{\textcolor{b l u e}{30 \times} 4 x}{15} - \frac{\textcolor{b l u e}{30 \times} 5}{6} = \frac{\textcolor{b l u e}{30 \times} 2}{3}$

$\frac{\textcolor{b l u e}{{\cancel{30}}^{2} \times} 4 x}{\cancel{15}} - \frac{\textcolor{b l u e}{{\cancel{30}}^{5} \times} 5}{\cancel{6}} = \frac{\textcolor{b l u e}{{\cancel{30}}^{10} \times} 2}{\cancel{3}}$

$8 x - 25 = 20$

$8 x = 20 + 25$

$8 x = 45$

$x = 5 \frac{5}{8} = 5.625$