Linear Algebra Examples

$9 = \frac{1}{5} z + 12$

Step 1

Rewrite the equation as $\frac{1}{5} z + 12 = 9$ .

$\frac{1}{5} z + 12 = 9$

Step 2

Combine $\frac{1}{5}$ and $z$ .

$\frac{z}{5} + 12 = 9$

Step 3

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

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Step 3.1

Subtract $12$ from both sides of the equation.

$\frac{z}{5} = 9 - 12$

Step 3.2

Subtract $12$ from $9$ .

$\frac{z}{5} = - 3$

Step 4

Multiply both sides of the equation by $5$ .

$5 \frac{z}{5} = 5 \cdot - 3$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1

Cancel the common factor.

$5 \frac{z}{5} = 5 \cdot - 3$

Step 5.1.1.2

Rewrite the expression.

$z = 5 \cdot - 3$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $5$ by $- 3$ .

$z = - 15$

Step 6

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

${z | z = - 15}$

Step 7