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

1 Answer
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  for 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!