Pre-Algebra Examples

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

Step 1

Simplify $\frac{1}{5} \cdot (n - 3)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (n - 3) = 2 n$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

Combine $\frac{1}{5}$ and $- 3$ .

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

Step 1.6

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

Subtract $2 n$ from both sides of the equation.

$\frac{n}{5} - \frac{3}{5} - 2 n = 0$

Step 2.2

To write $- 2 n$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{n}{5} - 2 n \cdot \frac{5}{5} - \frac{3}{5} = 0$

Step 2.3

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

$\frac{n}{5} + \frac{- 2 n \cdot 5}{5} - \frac{3}{5} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{n - 2 n \cdot 5}{5} - \frac{3}{5} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{n - 2 n \cdot 5 - 3}{5} = 0$

Step 2.6

Multiply $5$ by $- 2$ .

$\frac{n - 10 n - 3}{5} = 0$

Step 2.7

Subtract $10 n$ from $n$ .

$\frac{- 9 n - 3}{5} = 0$

Step 2.8

Factor $3$ out of $- 9 n - 3$ .

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Step 2.8.1

Factor $3$ out of $- 9 n$ .

$\frac{3 (- 3 n) - 3}{5} = 0$

Step 2.8.2

Factor $3$ out of $- 3$ .

$\frac{3 (- 3 n) + 3 (- 1)}{5} = 0$

Step 2.8.3

Factor $3$ out of $3 (- 3 n) + 3 (- 1)$ .

$\frac{3 (- 3 n - 1)}{5} = 0$

Step 2.9

Factor $- 1$ out of $- 3 n$ .

$\frac{3 (- (3 n) - 1)}{5} = 0$

Step 2.10

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{3 (- (3 n) - 1 (1))}{5} = 0$

Step 2.11

Factor $- 1$ out of $- (3 n) - 1 (1)$ .

$\frac{3 (- (3 n + 1))}{5} = 0$

Step 2.12

Rewrite $- (3 n + 1)$ as $- 1 (3 n + 1)$ .

$\frac{3 (- 1 (3 n + 1))}{5} = 0$

Step 2.13

Move the negative in front of the fraction.

$- \frac{3 (3 n + 1)}{5} = 0$

Step 3

Set the numerator equal to zero.

$3 (3 n + 1) = 0$

Step 4

Solve the equation for $n$ .

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Step 4.1

Divide each term in $3 (3 n + 1) = 0$ by $3$ and simplify.

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Step 4.1.1

Divide each term in $3 (3 n + 1) = 0$ by $3$ .

$\frac{3 (3 n + 1)}{3} = \frac{0}{3}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $3$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{3 (3 n + 1)}{3} = \frac{0}{3}$

Step 4.1.2.1.2

Divide $3 n + 1$ by $1$ .

$3 n + 1 = \frac{0}{3}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $0$ by $3$ .

$3 n + 1 = 0$

Step 4.2

Subtract $1$ from both sides of the equation.

$3 n = - 1$

Step 4.3

Divide each term in $3 n = - 1$ by $3$ and simplify.

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Step 4.3.1

Divide each term in $3 n = - 1$ by $3$ .

$\frac{3 n}{3} = \frac{- 1}{3}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{3 n}{3} = \frac{- 1}{3}$

Step 4.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 1}{3}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$n = - \frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{1}{3}$

Decimal Form:

$n = - 0.\overline{3}$