# How do you solve x/5 - x/2= 3 + (3x)/10?

Jul 8, 2016

$x = - 5$

#### Explanation:

To solve $\frac{x}{5} - \frac{x}{2} = 3 + \frac{3 x}{10}$

Begin by multiplying every term by the common denominator $\left(10\right)$
to eliminate the denominators

$\left(10\right) \frac{x}{5} - \left(10\right) \frac{x}{2} = \left(10\right) 3 + \left(10\right) \frac{3 x}{10}$

$\cancel{10} 2 \frac{x}{\cancel{5}} - \cancel{10} 5 \frac{x}{\cancel{2}} = \left(10\right) 3 + \cancel{10} \frac{3 x}{\cancel{10}}$

$2 x - 5 x = 30 + 3 x$

Combine like terms

$- 3 x = 30 + 3 x$

Use the additive inverse to combine the variables on one side

$- 3 x - 3 x = 30 \cancel{+ 3 x} \cancel{- 3 x}$

$- 6 x = 30$

Use the multiplicative inverse to isolate the variable

$\cancel{- 6} \frac{x}{\cancel{- 6}} = \frac{30}{-} 6$

$x = - 5$