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

Answer 1

Genesis Allen

#r=17/3#

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

18 is the LCM of 9 and 6.

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

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

Give out the bracket.

#rArr8=3r-9#

To both sides, add 9.

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

#rArr3r=17#

divide each side by three.

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

#rArrr=17/3#

#color(blue)"As a check"#

This value should be substituted into the right side of the equation; if it equals the left side, the problem has been solved.

#"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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Answer 2

Jameson Allen

To solve the equation ( \frac{4}{9} = \frac{r-3}{6} ), first, cross multiply to eliminate the fractions. Then, solve for ( r ).

( 4 \times 6 = 9 \times (r-3) )

( 24 = 9r - 27 )

( 9r = 24 + 27 )

( 9r = 51 )

( r = \frac{51}{9} )

( r = 5.67 )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.