How do you solve #\frac{1}{7}-3(\frac{3}{7}n=\frac{2}{7})#?

1 Answer
Ms. Worth
Dec 14, 2017

#n = - (1)/(9)#

Explanation:

I think the question might have a typo.

I wonder if the problem should be written like this:

#(1)/(7) − 3( (3) / (7) n) = (2)/(7)#

#To  solve  f#or #n#

1) Clear the fractions by multiplying all the terms on both sides
by #7# and letting the denominators cancel

#1 - 3(3n) = 2#

2) Clear the parentheses by distributing the #-3#

#1 - 9n = 2#

3) Subtract #1# from both sides to isolate the #-9n# term

#-9n = 1#

4) Divide both sides by #-9# to isolate #n#

#n = - (1)/(9)# #larr# answer
...............................

Check

The check looks like it's going to be a mess.
I would advise you not to do it if you are low on time or
if you have something better to do with your time.
Just take a chance that your answer is probably correct.

If you do want to check, here is how:

1) Sub in #-(1)/(9)# for #n# in the original equation

#(1)/(7) − 3( (3) / (7) n) = (2)/(7)#

#(1)/(7) − 3( (3) / (7)xx -(1)/(9) ) = (2)/(7)#

2) Do the multiplication inside the parentheses

#(1)/(7) − 3( - (1)/(21) ) = (2)/(7)#

3) Clear the parentheses by distributing the #- 3#

#(1)/(7) + (3)/(21) = (2)/(7)#

4) Reduce the fraction to lowest terms

#(1)/(7) + (1)/(7) = (2)/(7)#

5) Combine like terms

#(2)/(7) = (2)/(7)#

#Check!#

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