Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Cancel the common factor of $5$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

$3 N + 5 \cdot 2 - n = - 6 n$

Step 1.4

Multiply $5$ by $2$ .

$3 N + 10 - n = - 6 n$

Step 2

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

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Step 2.1

Subtract $10$ from both sides of the equation.

$3 N - n = - 6 n - 10$

Step 2.2

Add $n$ to both sides of the equation.

$3 N = - 6 n - 10 + n$

Step 2.3

Add $- 6 n$ and $n$ .

$3 N = - 5 n - 10$

Step 3

Divide each term in $3 N = - 5 n - 10$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 N = - 5 n - 10$ by $3$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $N$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative in front of the fraction.

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

Step 3.3.1.2

Move the negative in front of the fraction.

$N = - \frac{5 n}{3} - \frac{10}{3}$