Linear Algebra Examples

$9 = 6 + \frac{z - 8}{4}$

Step 1

Rewrite the equation as $6 + \frac{z - 8}{4} = 9$ .

$6 + \frac{z - 8}{4} = 9$

Step 2

Simplify $6 + \frac{z - 8}{4}$ .

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Step 2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$6 \cdot \frac{4}{4} + \frac{z - 8}{4} = 9$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine $6$ and $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{z - 8}{4} = 9$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{6 \cdot 4 + z - 8}{4} = 9$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Multiply $6$ by $4$ .

$\frac{24 + z - 8}{4} = 9$

Step 2.3.2

Subtract $8$ from $24$ .

$\frac{z + 16}{4} = 9$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{z + 16}{4} = 4 \cdot 9$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

$4 \frac{z + 16}{4} = 4 \cdot 9$

Step 4.1.1.2

Rewrite the expression.

$z + 16 = 4 \cdot 9$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $9$ .

$z + 16 = 36$

Step 5

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

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Step 5.1

Subtract $16$ from both sides of the equation.

$z = 36 - 16$

Step 5.2

Subtract $16$ from $36$ .

$z = 20$

Step 6

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

${z | z = 20}$

Step 7