Solve for n 3/5n-2=1/2(1/5n-6)+3/10n

$\frac{3}{5} n - 2 = \frac{1}{2} (\frac{1}{5} n - 6) + \frac{3}{10} n$

Step 1

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{1}{2} \cdot (\frac{1}{5} n - 6) + \frac{3}{10} n = \frac{3}{5} n - 2$

Step 2

Simplify $\frac{1}{2} \cdot (\frac{1}{5} n - 6) + \frac{3}{10} n$ .

Simplify each term.

Combine $\frac{1}{5}$ and $n$ .

$\frac{1}{2} \cdot (\frac{n}{5} - 6) + \frac{3}{10} n = \frac{3}{5} n - 2$

Apply the distributive property.

$\frac{1}{2} \cdot \frac{n}{5} + \frac{1}{2} \cdot - 6 + \frac{3}{10} n = \frac{3}{5} n - 2$

Multiply $\frac{1}{2} \cdot \frac{n}{5}$ .

Multiply $\frac{1}{2}$ by $\frac{n}{5}$ .

$\frac{n}{2 \cdot 5} + \frac{1}{2} \cdot - 6 + \frac{3}{10} n = \frac{3}{5} n - 2$

Multiply $2$ by $5$ .

$\frac{n}{10} + \frac{1}{2} \cdot - 6 + \frac{3}{10} n = \frac{3}{5} n - 2$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$\frac{n}{10} + \frac{1}{2} \cdot (2 (- 3)) + \frac{3}{10} n = \frac{3}{5} n - 2$

Cancel the common factor.

$\frac{n}{10} + \frac{1}{2} \cdot (2 \cdot - 3) + \frac{3}{10} n = \frac{3}{5} n - 2$

Rewrite the expression.

$\frac{n}{10} - 3 + \frac{3}{10} n = \frac{3}{5} n - 2$

Combine $\frac{3}{10}$ and $n$ .

$\frac{n}{10} - 3 + \frac{3 n}{10} = \frac{3}{5} n - 2$

Simplify terms.

Combine the numerators over the common denominator.

$- 3 + \frac{n + 3 n}{10} = \frac{3}{5} n - 2$

Add $n$ and $3 n$ .

$- 3 + \frac{4 n}{10} = \frac{3}{5} n - 2$

Cancel the common factor of $4$ and $10$ .

Factor $2$ out of $4 n$ .

$- 3 + \frac{2 (2 n)}{10} = \frac{3}{5} n - 2$

Cancel the common factors.

Factor $2$ out of $10$ .

$- 3 + \frac{2 (2 n)}{2 (5)} = \frac{3}{5} n - 2$

Cancel the common factor.

$- 3 + \frac{2 (2 n)}{2 \cdot 5} = \frac{3}{5} n - 2$

Rewrite the expression.

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

Step 3

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

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

Step 4

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

Subtract $\frac{3 n}{5}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $3 n$ from $2 n$ .

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

Move the negative in front of the fraction.

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

Step 5

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

Add $3$ to both sides of the equation.

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

Add $- 2$ and $3$ .

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

Step 6

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{n}{5}) = - 5 \cdot 1$

Step 7

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 5 (- \frac{n}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{n}{5}$ into the numerator.

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

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- n}{5} = - 5 \cdot 1$

Cancel the common factor.

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

Rewrite the expression.

$- - n = - 5 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 n = - 5 \cdot 1$

Multiply $n$ by $1$ .

$n = - 5 \cdot 1$

Simplify the right side.

Multiply $- 5$ by $1$ .

$n = - 5$

Solve for n 3/5n-2=1/2(1/5n-6)+3/10n

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