# How do you solve 5/8+3/4x=1/16?

Mar 26, 2016

$x = - \frac{3}{4}$

#### Explanation:

Notice that all the denominators are factors of 16

$\left(\frac{5}{8} \times \frac{2}{2}\right) + \left(\frac{3}{4} \times \frac{4}{4}\right) x = \frac{1}{6}$

'~~~~~~~~~~~~~~~~ Explaining an idea ~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\text{Note that "2/2" and "4/4" are equivalent to the value of 1}}$

color(brown)("So, in effect "5/8xx2/2" is equivalent to "5/8xx1" and ")
$\textcolor{b r o w n}{\frac{3}{4} \times \frac{4}{4} \text{ is equivalent to } \frac{3}{4} \times 1}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\frac{10}{16} + \frac{12}{16} x = \frac{1}{16}$

Multiply everything by 16

$10 + 12 x = 1$

Subtract 10 from both sides

$12 x = 1 - 10$

Divide both sides by 12

$x = - \frac{9}{12} = - \frac{3}{4}$