Pre-Algebra Examples

$\frac{6}{7} z - \frac{1}{7} z = - \frac{1}{8} - \frac{1}{x}$

Step 1

Simplify $\frac{6}{7} z - \frac{1}{7} z$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{6}{7}$ and $z$ .

$\frac{6 z}{7} - \frac{1}{7} z = - \frac{1}{8} - \frac{1}{x}$

Step 1.1.2

Combine $z$ and $\frac{1}{7}$ .

$\frac{6 z}{7} - \frac{z}{7} = - \frac{1}{8} - \frac{1}{x}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{6 z - z}{7} = - \frac{1}{8} - \frac{1}{x}$

Step 1.2.2

Subtract $z$ from $6 z$ .

$\frac{5 z}{7} = - \frac{1}{8} - \frac{1}{x}$

Step 2

Multiply both sides of the equation by $\frac{7}{5}$ .

$\frac{7}{5} \cdot \frac{5 z}{7} = \frac{7}{5} (- \frac{1}{8} - \frac{1}{x})$

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 $\frac{7}{5} \cdot \frac{5 z}{7}$ .

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Step 3.1.1.1

Cancel the common factor of $7$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{7}{5} \cdot \frac{5 z}{7} = \frac{7}{5} (- \frac{1}{8} - \frac{1}{x})$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 z) = \frac{7}{5} (- \frac{1}{8} - \frac{1}{x})$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Factor $5$ out of $5 z$ .

$\frac{1}{5} (5 (z)) = \frac{7}{5} (- \frac{1}{8} - \frac{1}{x})$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 z) = \frac{7}{5} (- \frac{1}{8} - \frac{1}{x})$

Step 3.1.1.2.3

Rewrite the expression.

$z = \frac{7}{5} (- \frac{1}{8} - \frac{1}{x})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{7}{5} (- \frac{1}{8} - \frac{1}{x})$ .

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Step 3.2.1.1

Apply the distributive property.

$z = \frac{7}{5} (- \frac{1}{8}) + \frac{7}{5} (- \frac{1}{x})$

Step 3.2.1.2

Multiply $\frac{7}{5} (- \frac{1}{8})$ .

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Step 3.2.1.2.1

Multiply $\frac{7}{5}$ by $\frac{1}{8}$ .

$z = - \frac{7}{5 \cdot 8} + \frac{7}{5} (- \frac{1}{x})$

Step 3.2.1.2.2

Multiply $5$ by $8$ .

$z = - \frac{7}{40} + \frac{7}{5} (- \frac{1}{x})$

Step 3.2.1.3

Multiply $\frac{7}{5}$ by $\frac{1}{x}$ .

$z = - \frac{7}{40} - \frac{7}{5 x}$