Algebra Examples

$a_{n} = - 5 n + 13$

Step 1

Solve the equation for $n$ .

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Step 1.1

Add $5 n$ to both sides of the equation.

$a_{n} + 5 n = 13$

Step 1.2

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

$5 n = 13 - a_{n}$

Step 1.3

Divide each term in $5 n = 13 - a_{n}$ by $5$ and simplify.

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Step 1.3.1

Divide each term in $5 n = 13 - a_{n}$ by $5$ .

$\frac{5 n}{5} = \frac{13}{5} + \frac{- a_{n}}{5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{5 n}{5} = \frac{13}{5} + \frac{- a_{n}}{5}$

Step 1.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{13}{5} + \frac{- a_{n}}{5}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$n = \frac{13}{5} - \frac{a_{n}}{5}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{13}{5} - \frac{- 5 n + 13}{5}$ .

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Step 2.1.1

Combine the numerators over the common denominator.

$n = \frac{13 - (- 5 n + 13)}{5}$

Step 2.1.2

Simplify each term.

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Step 2.1.2.1

Apply the distributive property.

$n = \frac{13 - (- 5 n) - 1 \cdot 13}{5}$

Step 2.1.2.2

Multiply $- 5$ by $- 1$ .

$n = \frac{13 + 5 n - 1 \cdot 13}{5}$

Step 2.1.2.3

Multiply $- 1$ by $13$ .

$n = \frac{13 + 5 n - 13}{5}$

Step 2.1.3

Simplify terms.

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Step 2.1.3.1

Combine the opposite terms in $13 + 5 n - 13$ .

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Step 2.1.3.1.1

Subtract $13$ from $13$ .

$n = \frac{5 n + 0}{5}$

Step 2.1.3.1.2

Add $5 n$ and $0$ .

$n = \frac{5 n}{5}$

Step 2.1.3.2

Cancel the common factor of $5$ .

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Step 2.1.3.2.1

Cancel the common factor.

$n = \frac{5 n}{5}$

Step 2.1.3.2.2

Divide $n$ by $1$ .

$n = n$