First we distribute [tex] \frac{1}{5} [/tex] into [tex]n[/tex] and [tex] -\frac{1}{7}[/tex].
[tex] \frac{1}{5} * n = \frac{1}{5} n [/tex]
[tex] \frac{1}{5} * -\frac{1}{7} = - \frac{1}{35} [/tex]
That makes the left side of the equation
[tex] \frac{1}{5} n - \frac{1}{35} = \frac{1}{6} n[/tex]
Now we subtract [tex] \frac{1}{5}n[/tex] from [tex] \frac{1}{6} n[/tex], which makes [tex] \frac{1}{30} [/tex]
Now the equation is
[tex] -\frac{1}{35} = -\frac{1}{30n} [/tex]
Our goal is to isolate [tex]n[/tex], so we both sides by 30
[tex]30* -\frac{1}{35} = - \frac{1}{30}n * 30[/tex]
That will make the equation
[tex]- \frac{30}{35} = -n[/tex]
We multiply -1 on both sides of the equation:
[tex] \frac{30}{35} = n[/tex]
Finally we simplify [tex] \frac{30}{35} [/tex], which makes [tex] \frac{6}{7} [/tex]
So the answer is [tex]n = \frac{6}{7} [/tex]
