# How do you solve \frac { 7} { 5} n - n = \frac { 4} { 5}?

Oct 9, 2017

$n = 2$

#### Explanation:

First, simplifying the LHS by combining the like terms:

$\setminus \frac{7}{5} n - n = \setminus \frac{2}{5} n$

We can rewrite the equation as:

$\setminus \frac{2}{5} n = \setminus \frac{4}{5}$

To isolate for $n$, we have to multiply by its coefficient's reciprocal:

$\left(\setminus \frac{5}{2}\right) \setminus \cdot \setminus \frac{2}{5} n = \setminus \frac{4}{5} \setminus \cdot \setminus \frac{5}{2}$

Which leaves us with:

$n = \setminus \frac{20}{10}$

Which simplifies to:

$n = 2$