Algebra Examples

$a_{n} = 3 n - 5$

Step 1

Solve the equation for $n$ .

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Step 1.1

Subtract $3 n$ from both sides of the equation.

$a_{n} - 3 n = - 5$

Step 1.2

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

$- 3 n = - 5 - a_{n}$

Step 1.3

Divide each term in $- 3 n = - 5 - a_{n}$ by $- 3$ and simplify.

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Step 1.3.1

Divide each term in $- 3 n = - 5 - a_{n}$ by $- 3$ .

$\frac{- 3 n}{- 3} = \frac{- 5}{- 3} + \frac{- a_{n}}{- 3}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 3 n}{- 3} = \frac{- 5}{- 3} + \frac{- a_{n}}{- 3}$

Step 1.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 5}{- 3} + \frac{- a_{n}}{- 3}$

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

Dividing two negative values results in a positive value.

$n = \frac{5}{3} + \frac{- a_{n}}{- 3}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

$n = \frac{5}{3} + \frac{a_{n}}{3}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{5}{3} + \frac{3 n - 5}{3}$ .

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Step 2.1.1

Combine the numerators over the common denominator.

$n = \frac{5 + 3 n - 5}{3}$

Step 2.1.2

Combine the opposite terms in $5 + 3 n - 5$ .

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Step 2.1.2.1

Subtract $5$ from $5$ .

$n = \frac{3 n + 0}{3}$

Step 2.1.2.2

Add $3 n$ and $0$ .

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

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

Cancel the common factor.

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

Step 2.1.3.2

Divide $n$ by $1$ .

$n = n$