Linear Algebra Examples

$- 3 + 8 n = - 5$

Step 1

Move all terms not containing $n$ to the right side of the equation.

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Step 1.1

Add $3$ to both sides of the equation.

$8 n = - 5 + 3$

Step 1.2

Add $- 5$ and $3$ .

$8 n = - 2$

Step 2

Divide each term in $8 n = - 2$ by $8$ and simplify.

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Step 2.1

Divide each term in $8 n = - 2$ by $8$ .

$\frac{8 n}{8} = \frac{- 2}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{8 n}{8} = \frac{- 2}{8}$

Step 2.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 2}{8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $- 2$ and $8$ .

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Step 2.3.1.1

Factor $2$ out of $- 2$ .

$n = \frac{2 (- 1)}{8}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $8$ .

$n = \frac{2 \cdot - 1}{2 \cdot 4}$

Step 2.3.1.2.2

Cancel the common factor.

$n = \frac{2 \cdot - 1}{2 \cdot 4}$

Step 2.3.1.2.3

Rewrite the expression.

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

Step 2.3.2

Move the negative in front of the fraction.

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

Step 3

The domain is the set of all valid $n$ values.

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

Step 4