How do you solve 1/(2x) + 2/x = 1/8?

Jan 30, 2017

$\text{the answer is x=20}$

Explanation:

$\text{given : } \frac{1}{2 x} + \frac{2}{x} = \frac{1}{8}$

$\textcolor{red}{\frac{4}{4}} \cdot \frac{1}{2 x} + \textcolor{b l u e}{\frac{8}{8}} \frac{.2}{x} = \textcolor{g r e e n}{\frac{x}{x}} \cdot \frac{1}{8}$

$\frac{4}{8 x} + \frac{16}{8 x} = \frac{x}{8 x}$

$\frac{4}{\cancel{\left(8 x\right)}} + \frac{16}{\cancel{\left(8 x\right)}} = \frac{x}{\cancel{\left(8 x\right)}}$

$4 + 16 = x$

$x = 20$

Jan 30, 2017

$x = 20$

Explanation:

$\frac{1}{2 x} + \frac{2}{x} = \frac{1}{8}$

$\therefore \frac{8 + 32 = 2 x}{16 x}$

$\therefore \frac{8}{16 x} + \frac{32}{16 x} = \frac{2 x}{16 x}$

$\therefore 8 + 32 = 2 x$

$\therefore 2 x = 40$

$\therefore x = 20$

substitute x = 20

$\therefore \frac{1}{2 \left(20\right)} + \frac{2}{20} = \frac{1}{8}$

$\therefore \frac{\left(1 + 4\right) = 5}{40}$

$\therefore \frac{1}{40} + \frac{4}{40} = \frac{5}{40}$

$\therefore \frac{5}{40} = \frac{5}{40}$
or
$\frac{1}{8} = \frac{1}{8}$