Algebra Examples

$a_{n} = n - 5$

Step 1

Solve the equation for $n$ .

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Step 1.1

Subtract $n$ from both sides of the equation.

$a_{n} - n = - 5$

Step 1.2

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

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

Step 1.3

Divide each term in $- n = - 5 - a_{n}$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- n = - 5 - a_{n}$ by $- 1$ .

$\frac{- n}{- 1} = \frac{- 5}{- 1} + \frac{- a_{n}}{- 1}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{- 5}{- 1} + \frac{- a_{n}}{- 1}$

Step 1.3.2.2

Divide $n$ by $1$ .

$n = \frac{- 5}{- 1} + \frac{- a_{n}}{- 1}$

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

Divide $- 5$ by $- 1$ .

$n = 5 + \frac{- a_{n}}{- 1}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

$n = 5 + \frac{a_{n}}{1}$

Step 1.3.3.1.3

Divide $a_{n}$ by $1$ .

$n = 5 + a_{n}$

Step 2

Substitute the calculated values for $a_{n}$ into the equation for $n$ .

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Step 2.1

Simplify the left side.

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Step 2.1.1

Remove parentheses.

$n = 5 + n - 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Subtract $5$ from $5$ .

$n = n + 0$

Step 2.2.1.2

Add $n$ and $0$ .

$n = n$