# How do you solve 4/9 = r - 3 / 6?

Mar 14, 2018

$r = \frac{17}{18}$

#### Explanation:

$\text{multiply all terms by the "color(blue)"lowest common multiple}$
$\text{of 9 and 6 which is 18}$

${\cancel{18}}^{2} \times \frac{4}{\cancel{9}} ^ 1 = 18 r - \left({\cancel{18}}^{3} \times \frac{3}{\cancel{6}} ^ 1\right)$

$\Rightarrow 8 = 18 r - 9$

$\text{add 9 to both sides}$

$8 + 9 = 18 r \cancel{- 9} \cancel{+ 9}$

$\Rightarrow 18 r = 17$

$\text{divide both sides by 18}$

$\frac{\cancel{18} r}{\cancel{18}} = \frac{17}{18}$

$\Rightarrow r = \frac{17}{18}$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the right side of the equation and if equal to the left side then it is the solution.

$\text{right side "=17/18-9/18=8/18=4/9=" left side}$

$\Rightarrow r = \frac{17}{18} \text{ is the solution}$