Question

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

Answer 1

`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!`