Answer:
value of n = 2
Step-by-step explanation:
[tex]\frac{4}{5n}-\frac{1}{5}=\frac{2}{5n}[/tex]
We need to solve the above equation.
Find Least Common multiplier from 5n, 5 = 5n
Multiply both sides of the equation by 5n
[tex]\frac{4}{5n}*5n-\frac{1}{5}*5n=\frac{2}{5n}*5n\\Solving:\\4 -n = 2\\[/tex]
Now finding the value of n.
Adding -4 on both sides
[tex]4 -n-4 = 2-4\\-n= -2[/tex]
Multiplying both sides by -1
n = 2
The value of n is 2.
We can verify by putting value of n in the given question.
[tex]\frac{4}{5n}-\frac{1}{5}=\frac{2}{5n}\\n=2\\\frac{4}{5*2}-\frac{1}{5}=\frac{2}{5*2}\\\frac{4}{10}-\frac{1}{5}=\frac{2}{10}\\\frac{2}{5}-\frac{1}{5}=\frac{1}{5}\\\frac{2-1}{5}=\frac{1}{5}\\\frac{1}{5}=\frac{1}{5}[/tex]
So, value of n = 2
