Algebra Examples

$a_{n} = 4 n + 1$

Step 1

Solve the equation for $n$ .

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Step 1.1

Subtract $4 n$ from both sides of the equation.

$a_{n} - 4 n = 1$

Step 1.2

Subtract $a_{n}$ from both sides of the equation.

$- 4 n = 1 - a_{n}$

Step 1.3

Divide each term in $- 4 n = 1 - a_{n}$ by $- 4$ and simplify.

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Step 1.3.1

Divide each term in $- 4 n = 1 - a_{n}$ by $- 4$ .

$\frac{- 4 n}{- 4} = \frac{1}{- 4} + \frac{- a_{n}}{- 4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 4 n}{- 4} = \frac{1}{- 4} + \frac{- a_{n}}{- 4}$

Step 1.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{1}{- 4} + \frac{- a_{n}}{- 4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative in front of the fraction.

$n = - \frac{1}{4} + \frac{- a_{n}}{- 4}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

$n = - \frac{1}{4} + \frac{a_{n}}{4}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $- \frac{1}{4} + \frac{4 n + 1}{4}$ .

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Step 2.1.1

Combine the numerators over the common denominator.

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

Step 2.1.2

Combine the opposite terms in $- 1 + 4 n + 1$ .

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Step 2.1.2.1

Add $- 1$ and $1$ .

$n = \frac{4 n + 0}{4}$

Step 2.1.2.2

Add $4 n$ and $0$ .

$n = \frac{4 n}{4}$

Step 2.1.3

Cancel the common factor of $4$ .

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Step 2.1.3.1

Cancel the common factor.

$n = \frac{4 n}{4}$

Step 2.1.3.2

Divide $n$ by $1$ .

$n = n$