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

Dec 14, 2017

$n = - \frac{1}{9}$

#### 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

$1 - 3 \left(3 n\right) = 2$

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

$1 - 9 n = 2$

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

$- 9 n = 1$

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

$n = - \frac{1}{9}$ $\leftarrow$ 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.

If you do want to check, here is how:

1) Sub in $- \frac{1}{9}$ 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 $- 3$

$\frac{1}{7} + \frac{3}{21} = \frac{2}{7}$

4) Reduce the fraction to lowest terms

$\frac{1}{7} + \frac{1}{7} = \frac{2}{7}$

5) Combine like terms

$\frac{2}{7} = \frac{2}{7}$

Check!