# 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.
Just take a chance that your answer is probably correct.

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!