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

1 Answer
Jim G.
Apr 15, 2017

#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"#

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