Algebra Examples

$y_{n} = - 5 n - 5$

Step 1

Solve the equation for $n$ .

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Step 1.1

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

$y_{n} + 5 n = - 5$

Step 1.2

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

$5 n = - 5 - y_{n}$

Step 1.3

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

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Step 1.3.1

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

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

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.

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

Step 1.3.2.1.2

Divide $n$ by $1$ .

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

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

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

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 $5$ .

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

Step 1.3.3.1.2

Move the negative in front of the fraction.

$n = - 1 - \frac{y_{n}}{5}$

$n = - 1 - \frac{y_{n}}{5}$

$n = - 1 - \frac{y_{n}}{5}$

$n = - 1 - \frac{y_{n}}{5}$

$n = - 1 - \frac{y_{n}}{5}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $- 1 - \frac{- 5 n - 5}{5}$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Cancel the common factor of $- 5 n - 5$ and $5$ .

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Step 2.1.1.1.1

Factor $5$ out of $- 5 n$ .

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

Step 2.1.1.1.2

Factor $5$ out of $- 5$ .

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

Step 2.1.1.1.3

Factor $5$ out of $5 (- n) + 5 (- 1)$ .

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

Step 2.1.1.1.4

Cancel the common factors.

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Step 2.1.1.1.4.1

Factor $5$ out of $5$ .

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

Step 2.1.1.1.4.2

Cancel the common factor.

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

Step 2.1.1.1.4.3

Rewrite the expression.

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

Step 2.1.1.1.4.4

Divide $- n - 1$ by $1$ .

$n = - 1 - (- n - 1)$

$n = - 1 - (- n - 1)$

$n = - 1 - (- n - 1)$

Step 2.1.1.2

Apply the distributive property.

$n = - 1 - - n - - 1$

Step 2.1.1.3

Multiply $- - n$ .

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Step 2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$n = - 1 + 1 n - - 1$

Step 2.1.1.3.2

Multiply $n$ by $1$ .

$n = - 1 + n - - 1$

$n = - 1 + n - - 1$

Step 2.1.1.4

Multiply $- 1$ by $- 1$ .

$n = - 1 + n + 1$

$n = - 1 + n + 1$

Step 2.1.2

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

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Step 2.1.2.1

Add $- 1$ and $1$ .

$n = n + 0$

Step 2.1.2.2

Add $n$ and $0$ .

$n = n$

$n = n$

$n = n$

$n = n$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$