Precalculus Examples

$n = 4 + \frac{4}{3} \cdot (n - 1)$

Step 1

Simplify $4 + \frac{4}{3} \cdot (n - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$n = 4 + \frac{4}{3} n + \frac{4}{3} \cdot - 1$

Step 1.1.2

Combine $\frac{4}{3}$ and $n$ .

$n = 4 + \frac{4 n}{3} + \frac{4}{3} \cdot - 1$

Step 1.1.3

Multiply $\frac{4}{3} \cdot - 1$ .

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Step 1.1.3.1

Combine $\frac{4}{3}$ and $- 1$ .

$n = 4 + \frac{4 n}{3} + \frac{4 \cdot - 1}{3}$

Step 1.1.3.2

Multiply $4$ by $- 1$ .

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

Step 1.1.4

Move the negative in front of the fraction.

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

Step 1.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

Combine $4$ and $\frac{3}{3}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $4$ by $3$ .

$n = \frac{4 n}{3} + \frac{12 - 4}{3}$

Step 1.5.2

Subtract $4$ from $12$ .

$n = \frac{4 n}{3} + \frac{8}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{4 n}{3}$ from both sides of the equation.

$n - \frac{4 n}{3} = \frac{8}{3}$

Step 2.2

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

$n \cdot \frac{3}{3} - \frac{4 n}{3} = \frac{8}{3}$

Step 2.3

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

$\frac{n \cdot 3}{3} - \frac{4 n}{3} = \frac{8}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{n \cdot 3 - 4 n}{3} = \frac{8}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $3$ to the left of $n$ .

$\frac{3 \cdot n - 4 n}{3} = \frac{8}{3}$

Step 2.5.2

Subtract $4 n$ from $3 n$ .

$\frac{- n}{3} = \frac{8}{3}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{n}{3} = \frac{8}{3}$

Step 3

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

$- n = 8$

Step 4

Divide each term in $- n = 8$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- n = 8$ by $- 1$ .

$\frac{- n}{- 1} = \frac{8}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{8}{- 1}$

Step 4.2.2

Divide $n$ by $1$ .

$n = \frac{8}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $8$ by $- 1$ .

$n = - 8$