Algebra Examples

$A (n) = 5 + (n - 1) (\frac{1}{6})$

Step 1

Write $A (n) = 5 + (n - 1) (\frac{1}{6})$ as an equation.

$y = 5 + (n - 1) (\frac{1}{6})$

Step 2

Simplify $5 + (n - 1) (\frac{1}{6})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$y = 5 + n \frac{1}{6} - 1 (\frac{1}{6})$

Step 2.1.2

Combine $n$ and $\frac{1}{6}$ .

$y = 5 + \frac{n}{6} - 1 (\frac{1}{6})$

Step 2.1.3

Rewrite $- 1 (\frac{1}{6})$ as $- (\frac{1}{6})$ .

$y = 5 + \frac{n}{6} - \frac{1}{6}$

Step 2.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = \frac{n}{6} + 5 \cdot \frac{6}{6} - \frac{1}{6}$

Step 2.3

Combine $5$ and $\frac{6}{6}$ .

$y = \frac{n}{6} + \frac{5 \cdot 6}{6} - \frac{1}{6}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{n}{6} + \frac{5 \cdot 6 - 1}{6}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $5$ by $6$ .

$y = \frac{n}{6} + \frac{30 - 1}{6}$

Step 2.5.2

Subtract $1$ from $30$ .

$y = \frac{n}{6} + \frac{29}{6}$

Step 3

Choose any value for $n$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $n$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = \frac{0}{6} + \frac{29}{6}$

Step 4.2

Simplify $\frac{0}{6} + \frac{29}{6}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{0 + 29}{6}$

Step 4.2.2

Add $0$ and $29$ .

$y = \frac{29}{6}$

Step 4.3

Use the $n$ and $y$ values to form the ordered pair.

$(0, \frac{29}{6})$

Step 5

Choose $1$ to substitute in for $n$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = \frac{1}{6} + \frac{29}{6}$

Step 5.2

Simplify $\frac{1}{6} + \frac{29}{6}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{1 + 29}{6}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Add $1$ and $29$ .

$y = \frac{30}{6}$

Step 5.2.2.2

Divide $30$ by $6$ .

$y = 5$

Step 5.3

Use the $n$ and $y$ values to form the ordered pair.

$(1, 5)$

Step 6

Choose $2$ to substitute in for $n$ to find the ordered pair.

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Step 6.1

Remove parentheses.

$y = \frac{2}{6} + \frac{29}{6}$

Step 6.2

Simplify $\frac{2}{6} + \frac{29}{6}$ .

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Step 6.2.1

Combine the numerators over the common denominator.

$y = \frac{2 + 29}{6}$

Step 6.2.2

Add $2$ and $29$ .

$y = \frac{31}{6}$

Step 6.3

Use the $n$ and $y$ values to form the ordered pair.

$(2, \frac{31}{6})$

Step 7

These are three possible solutions to the equation.

$(0, \frac{29}{6}), (1, 5), (2, \frac{31}{6})$

Step 8