Question

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

Answer 1

`r=17/3`

Explanation:

To eliminate the fractions, multiply both sides by the `color(blue)"lowest common multiple"` (LCM) of 9 and 6

The LCM of 9 and 6 is 18

`cancel(18)^2xx4/cancel(9)^1=cancel(18)^3xx((r-3))/cancel(6)^1`

`rArr8=3(r-3)larrcolor(red)" no fractions"`

distribute the bracket.

`rArr8=3r-9`

add 9 to both sides.

`8+9=3rcancel(-9)cancel(+9)`

`rArr3r=17`

divide both sides by 3

`(cancel(3) r)/cancel(3)=17/3`

`rArrr=17/3`

`color(blue)"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.

`"right side " =(17/3-9/3)/6=8/3xx1/6=8/18=4/9=" left side"`

`rArrr=17/3" is the solution"`