# How do you solve (1/3)-(x/5)=(1/2)-(x/10)?

May 18, 2017

$x = - \frac{5}{3}$

#### Explanation:

Whenever you have fractions in an equation, you can get rid of them in the very beginning.

Do this by multiplying each fraction by the LCM of the denominators.

This means, find a number which ALL the denominators can divide into. In this case it is $\textcolor{m a \ge n t a}{30}$

$\frac{\textcolor{m a \ge n t a}{30} \times 1}{3} - \frac{\textcolor{m a \ge n t a}{30 \times} x}{5} = \frac{\textcolor{m a \ge n t a}{30 \times} 1}{2} - \frac{\textcolor{m a \ge n t a}{30 \times} x}{10}$

Now cancel all the denominators with the color(magenta)(30 then simplify.

$\frac{\textcolor{m a \ge n t a}{{\cancel{30}}^{10}} \times 1}{\cancel{3}} - \frac{\textcolor{m a \ge n t a}{{\cancel{30}}^{6} \times} x}{\cancel{5}} = \frac{\textcolor{m a \ge n t a}{{\cancel{30}}^{15} \times} 1}{\cancel{2}} - \frac{\textcolor{m a \ge n t a}{{\cancel{30}}^{3} \times} x}{\cancel{10}}$

$\textcolor{w h i t e}{\ldots . .} 10 \textcolor{w h i t e}{\ldots \ldots \ldots .} - 6 x \textcolor{w h i t e}{\ldots . .} = \textcolor{w h i t e}{\ldots . .} 15 \textcolor{w h i t e}{\ldots \ldots \ldots . .} - 3 x$

Now solve the equation as usual- there are no fractions.

$10 - 6 x = 15 - 3 x \text{ }$ add $6 x$ and subtract $15$ on both sides

$10 - 15 = - 3 x + 6 x$

$- 5 = 3 x$

$x = - \frac{5}{3}$