Basic Math Examples

$8 = \frac{1}{z + 6}$

Step 1

Rewrite the equation as $\frac{1}{z + 6} = 8$ .

$\frac{1}{z + 6} = 8$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$z + 6, 1$

Step 2.2

Remove parentheses.

$z + 6, 1$

Step 2.3

The LCM of one and any expression is the expression.

$z + 6$

Step 3

Multiply each term in $\frac{1}{z + 6} = 8$ by $z + 6$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1}{z + 6} = 8$ by $z + 6$ .

$\frac{1}{z + 6} (z + 6) = 8 (z + 6)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $z + 6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1}{z + 6} (z + 6) = 8 (z + 6)$

Step 3.2.1.2

Rewrite the expression.

$1 = 8 (z + 6)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$1 = 8 z + 8 \cdot 6$

Step 3.3.2

Multiply $8$ by $6$ .

$1 = 8 z + 48$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $8 z + 48 = 1$ .

$8 z + 48 = 1$

Step 4.2

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

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Step 4.2.1

Subtract $48$ from both sides of the equation.

$8 z = 1 - 48$

Step 4.2.2

Subtract $48$ from $1$ .

$8 z = - 47$

Step 4.3

Divide each term in $8 z = - 47$ by $8$ and simplify.

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Step 4.3.1

Divide each term in $8 z = - 47$ by $8$ .

$\frac{8 z}{8} = \frac{- 47}{8}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $8$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{8 z}{8} = \frac{- 47}{8}$

Step 4.3.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 47}{8}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$z = - \frac{47}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{47}{8}$

Decimal Form:

$z = - 5.875$

Mixed Number Form:

$z = - 5 \frac{7}{8}$