Question

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

Answer 1

`r=17/18`

Explanation:

`"multiply all terms by the "color(blue)"lowest common multiple"`
`"of 9 and 6 which is 18"`

`cancel(18)^2xx4/cancel(9)^1=18r-(cancel(18)^3xx3/cancel(6)^1)`

`rArr8=18r-9`

`"add 9 to both sides"`

`8+9=18rcancel(-9)cancel(+9)`

`rArr18r=17`

`"divide both sides by 18"`

`(cancel(18) r)/cancel(18)=17/18`

`rArrr=17/18`

`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 "=17/18-9/18=8/18=4/9=" left side"`

`rArrr=17/18" is the solution"`