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

Apr 15, 2017

$r = \frac{17}{3}$

#### Explanation:

To eliminate the fractions, multiply both sides by the $\textcolor{b l u e}{\text{lowest common multiple}}$ (LCM) of 9 and 6

The LCM of 9 and 6 is 18

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

$\Rightarrow 8 = 3 \left(r - 3\right) \leftarrow \textcolor{red}{\text{ no fractions}}$

distribute the bracket.

$\Rightarrow 8 = 3 r - 9$

$8 + 9 = 3 r \cancel{- 9} \cancel{+ 9}$

$\Rightarrow 3 r = 17$

divide both sides by 3

$\frac{\cancel{3} r}{\cancel{3}} = \frac{17}{3}$

$\Rightarrow r = \frac{17}{3}$

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

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

$\text{right side " =(17/3-9/3)/6=8/3xx1/6=8/18=4/9=" left side}$

$\Rightarrow r = \frac{17}{3} \text{ is the solution}$