How do you solve #4/(9y-6)=2#?

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Answer 1 · 2016-02-06T02:28:46

Step by step explanation is given blow

#4/(9y-6) = 2#

Think of this as a proportion

#4/(9y-6)=2/1#

We know if #a/b = c/d# Then #b/a = d/c#

Basically we are flipping and that would help us

#(9y-6)/4=1/2#

Let us multiply #4# on both the sides

#cancel(4)xx(9y-6)/cancel(4)=4xx1/2#

#9y-6 = 2#

To solve for #y# we need to undo all that has been done to it, for this we shall use the inverse operations.

Let us start with #-6# we add #6# on both the sides and we get

#9y-cancel(6)+cancel(6) = 2+6#
#9y=8#

#y# is multiplied by #9# to undo it we divide both sides by #9#

#(cancel(9)y)/cancel(9) =8/9#

#y=8/9#

Let us check if our solution is correct by plugging #y=8/9# in the original problem.

#4/(9y-6) = 2#
#4/(9(8/9)-6)=2#
#4/(8-6)=2#
#4/2=2#
#2=2 quad# this is a true statement so the solution is valid.

#y=8/9#