Basic Math Examples

$\frac{9 z}{14} - \frac{z}{7} = 1$

Step 1

Simplify $\frac{9 z}{14} - \frac{z}{7}$ .

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Step 1.1

To write $- \frac{z}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 z}{14} - \frac{z}{7} \cdot \frac{2}{2} = 1$

Step 1.2

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{z}{7}$ by $\frac{2}{2}$ .

$\frac{9 z}{14} - \frac{z \cdot 2}{7 \cdot 2} = 1$

Step 1.2.2

Multiply $7$ by $2$ .

$\frac{9 z}{14} - \frac{z \cdot 2}{14} = 1$

Step 1.3

Combine the numerators over the common denominator.

$\frac{9 z - z \cdot 2}{14} = 1$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $z$ out of $9 z - z \cdot 2$ .

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Step 1.4.1.1

Factor $z$ out of $9 z$ .

$\frac{z \cdot 9 - z \cdot 2}{14} = 1$

Step 1.4.1.2

Factor $z$ out of $- z \cdot 2$ .

$\frac{z \cdot 9 + z (- 1 \cdot 2)}{14} = 1$

Step 1.4.1.3

Factor $z$ out of $z \cdot 9 + z (- 1 \cdot 2)$ .

$\frac{z (9 - 1 \cdot 2)}{14} = 1$

Step 1.4.2

Multiply $- 1$ by $2$ .

$\frac{z (9 - 2)}{14} = 1$

Step 1.4.3

Subtract $2$ from $9$ .

$\frac{z \cdot 7}{14} = 1$

Step 1.5

Cancel the common factor of $7$ and $14$ .

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Step 1.5.1

Factor $7$ out of $z \cdot 7$ .

$\frac{7 \cdot z}{14} = 1$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $7$ out of $14$ .

$\frac{7 \cdot z}{7 \cdot 2} = 1$

Step 1.5.2.2

Cancel the common factor.

$\frac{7 \cdot z}{7 \cdot 2} = 1$

Step 1.5.2.3

Rewrite the expression.

$\frac{z}{2} = 1$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{z}{2} = 2 \cdot 1$

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

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$2 \frac{z}{2} = 2 \cdot 1$

Step 3.1.1.2

Rewrite the expression.

$z = 2 \cdot 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $1$ .

$z = 2$