Basic Math Examples

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

Step 1

Simplify $\frac{z}{8} - z$ .

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Step 1.1

To write $- z$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $- z$ and $\frac{8}{8}$ .

$\frac{z}{8} + \frac{- z \cdot 8}{8} = 7$

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.3

Simplify the numerator.

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Step 1.3.1

Factor $z$ out of $z - z \cdot 8$ .

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Step 1.3.1.1

Raise $z$ to the power of $1$ .

$\frac{z^{1} - z \cdot 8}{8} = 7$

Step 1.3.1.2

Factor $z$ out of $z^{1}$ .

$\frac{z \cdot 1 - z \cdot 8}{8} = 7$

Step 1.3.1.3

Factor $z$ out of $- z \cdot 8$ .

$\frac{z \cdot 1 + z (- 1 \cdot 8)}{8} = 7$

Step 1.3.1.4

Factor $z$ out of $z \cdot 1 + z (- 1 \cdot 8)$ .

$\frac{z (1 - 1 \cdot 8)}{8} = 7$

Step 1.3.2

Multiply $- 1$ by $8$ .

$\frac{z (1 - 8)}{8} = 7$

Step 1.3.3

Subtract $8$ from $1$ .

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

Step 1.4

Simplify the expression.

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Step 1.4.1

Move $- 7$ to the left of $z$ .

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

Step 1.4.2

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $- \frac{8}{7}$ .

$- \frac{8}{7} (- \frac{7 z}{8}) = - \frac{8}{7} \cdot 7$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- \frac{8}{7} (- \frac{7 z}{8})$ .

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Step 3.1.1.1

Cancel the common factor of $8$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{8}{7}$ into the numerator.

$\frac{- 8}{7} (- \frac{7 z}{8}) = - \frac{8}{7} \cdot 7$

Step 3.1.1.1.2

Move the leading negative in $- \frac{7 z}{8}$ into the numerator.

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

Step 3.1.1.1.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{7} \cdot \frac{- 7 z}{8} = - \frac{8}{7} \cdot 7$

Step 3.1.1.1.4

Cancel the common factor.

$\frac{8 \cdot - 1}{7} \cdot \frac{- 7 z}{8} = - \frac{8}{7} \cdot 7$

Step 3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 z) = - \frac{8}{7} \cdot 7$

Step 3.1.1.2

Cancel the common factor of $7$ .

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Step 3.1.1.2.1

Factor $7$ out of $- 7 z$ .

$\frac{- 1}{7} (7 (- z)) = - \frac{8}{7} \cdot 7$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- z)) = - \frac{8}{7} \cdot 7$

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{8}{7} \cdot 7$

Step 3.1.1.3.2

Multiply $z$ by $1$ .

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Move the leading negative in $- \frac{8}{7}$ into the numerator.

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

Step 3.2.1.2

Cancel the common factor.

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

Step 3.2.1.3

Rewrite the expression.

$z = - 8$