Pre-Algebra Examples

$\frac{2}{3} \cdot (n - 6) = 5 n - 43$

Step 1

Simplify $\frac{2}{3} \cdot (n - 6)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (n - 6) = 5 n - 43$

Step 1.2

Simplify by adding zeros.

$\frac{2}{3} \cdot (n - 6) = 5 n - 43$

Step 1.3

Apply the distributive property.

$\frac{2}{3} n + \frac{2}{3} \cdot - 6 = 5 n - 43$

Step 1.4

Combine $\frac{2}{3}$ and $n$ .

$\frac{2 n}{3} + \frac{2}{3} \cdot - 6 = 5 n - 43$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 6$ .

$\frac{2 n}{3} + \frac{2}{3} \cdot (3 (- 2)) = 5 n - 43$

Step 1.5.2

Cancel the common factor.

$\frac{2 n}{3} + \frac{2}{3} \cdot (3 \cdot - 2) = 5 n - 43$

Step 1.5.3

Rewrite the expression.

$\frac{2 n}{3} + 2 \cdot - 2 = 5 n - 43$

Step 1.6

Multiply $2$ by $- 2$ .

$\frac{2 n}{3} - 4 = 5 n - 43$

Step 2

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

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Step 2.1

Subtract $5 n$ from both sides of the equation.

$\frac{2 n}{3} - 4 - 5 n = - 43$

Step 2.2

To write $- 5 n$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 n}{3} - 5 n \cdot \frac{3}{3} - 4 = - 43$

Step 2.3

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

$\frac{2 n}{3} + \frac{- 5 n \cdot 3}{3} - 4 = - 43$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 n - 5 n \cdot 3}{3} - 4 = - 43$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $n$ out of $2 n - 5 n \cdot 3$ .

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Step 2.5.1.1.1

Factor $n$ out of $2 n$ .

$\frac{n \cdot 2 - 5 n \cdot 3}{3} - 4 = - 43$

Step 2.5.1.1.2

Factor $n$ out of $- 5 n \cdot 3$ .

$\frac{n \cdot 2 + n (- 5 \cdot 3)}{3} - 4 = - 43$

Step 2.5.1.1.3

Factor $n$ out of $n \cdot 2 + n (- 5 \cdot 3)$ .

$\frac{n (2 - 5 \cdot 3)}{3} - 4 = - 43$

Step 2.5.1.2

Multiply $- 5$ by $3$ .

$\frac{n (2 - 15)}{3} - 4 = - 43$

Step 2.5.1.3

Subtract $15$ from $2$ .

$\frac{n \cdot - 13}{3} - 4 = - 43$

Step 2.5.2

Move $- 13$ to the left of $n$ .

$\frac{- 13 \cdot n}{3} - 4 = - 43$

Step 2.5.3

Move the negative in front of the fraction.

$- \frac{13 n}{3} - 4 = - 43$

Step 3

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

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Step 3.1

Add $4$ to both sides of the equation.

$- \frac{13 n}{3} = - 43 + 4$

Step 3.2

Add $- 43$ and $4$ .

$- \frac{13 n}{3} = - 39$

Step 4

Multiply both sides of the equation by $- \frac{3}{13}$ .

$- \frac{3}{13} (- \frac{13 n}{3}) = - \frac{3}{13} \cdot - 39$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{3}{13} (- \frac{13 n}{3})$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{3}{13}$ into the numerator.

$\frac{- 3}{13} (- \frac{13 n}{3}) = - \frac{3}{13} \cdot - 39$

Step 5.1.1.1.2

Move the leading negative in $- \frac{13 n}{3}$ into the numerator.

$\frac{- 3}{13} \cdot \frac{- 13 n}{3} = - \frac{3}{13} \cdot - 39$

Step 5.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{13} \cdot \frac{- 13 n}{3} = - \frac{3}{13} \cdot - 39$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{13} \cdot \frac{- 13 n}{3} = - \frac{3}{13} \cdot - 39$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{13} (- 13 n) = - \frac{3}{13} \cdot - 39$

Step 5.1.1.2

Cancel the common factor of $13$ .

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Step 5.1.1.2.1

Factor $13$ out of $- 13 n$ .

$\frac{- 1}{13} (13 (- n)) = - \frac{3}{13} \cdot - 39$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{13} (13 (- n)) = - \frac{3}{13} \cdot - 39$

Step 5.1.1.2.3

Rewrite the expression.

$- - n = - \frac{3}{13} \cdot - 39$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 n = - \frac{3}{13} \cdot - 39$

Step 5.1.1.3.2

Multiply $n$ by $1$ .

$n = - \frac{3}{13} \cdot - 39$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{3}{13} \cdot - 39$ .

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Step 5.2.1.1

Cancel the common factor of $13$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{3}{13}$ into the numerator.

$n = \frac{- 3}{13} \cdot - 39$

Step 5.2.1.1.2

Factor $13$ out of $- 39$ .

$n = \frac{- 3}{13} \cdot (13 (- 3))$

Step 5.2.1.1.3

Cancel the common factor.

$n = \frac{- 3}{13} \cdot (13 \cdot - 3)$

Step 5.2.1.1.4

Rewrite the expression.

$n = - 3 \cdot - 3$

Step 5.2.1.2

Multiply $- 3$ by $- 3$ .

$n = 9$