Solve for n 2/5+3/5n-11/5=2/5n+1/5

$\frac{2}{5} + \frac{3}{5} n - \frac{11}{5} = \frac{2}{5} n + \frac{1}{5}$

Step 1

Simplify $\frac{2}{5} + \frac{3}{5} n - \frac{11}{5}$ .

Combine fractions.

Combine the numerators over the common denominator.

$\frac{3}{5} n + \frac{2 - 11}{5} = \frac{2}{5} n + \frac{1}{5}$

Subtract $11$ from $2$ .

$\frac{3}{5} n + \frac{- 9}{5} = \frac{2}{5} n + \frac{1}{5}$

Simplify each term.

Combine $\frac{3}{5}$ and $n$ .

$\frac{3 n}{5} + \frac{- 9}{5} = \frac{2}{5} n + \frac{1}{5}$

Move the negative in front of the fraction.

$\frac{3 n}{5} - \frac{9}{5} = \frac{2}{5} n + \frac{1}{5}$

Step 2

Combine $\frac{2}{5}$ and $n$ .

$\frac{3 n}{5} - \frac{9}{5} = \frac{2 n}{5} + \frac{1}{5}$

Step 3

Move all terms containing $n$ to the left side of the equation.

Subtract $\frac{2 n}{5}$ from both sides of the equation.

$\frac{3 n}{5} - \frac{9}{5} - \frac{2 n}{5} = \frac{1}{5}$

Combine the numerators over the common denominator.

$\frac{3 n - 9 - 2 n}{5} = \frac{1}{5}$

Subtract $2 n$ from $3 n$ .

$\frac{n - 9}{5} = \frac{1}{5}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$n - 9 = 1$

Step 5

Move all terms not containing $n$ to the right side of the equation.

Add $9$ to both sides of the equation.

$n = 1 + 9$

Add $1$ and $9$ .

$n = 10$