Basic Math Examples

$z + \frac{z}{4} = 14 - \frac{z}{2}$

Step 1

Simplify $z + \frac{z}{4}$ .

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Step 1.1

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

$z \cdot \frac{4}{4} + \frac{z}{4} = 14 - \frac{z}{2}$

Step 1.2

Simplify terms.

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Step 1.2.1

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

$\frac{z \cdot 4}{4} + \frac{z}{4} = 14 - \frac{z}{2}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{z \cdot 4 + z}{4} = 14 - \frac{z}{2}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Move $4$ to the left of $z$ .

$\frac{4 \cdot z + z}{4} = 14 - \frac{z}{2}$

Step 1.3.2

Add $4 z$ and $z$ .

$\frac{5 z}{4} = 14 - \frac{z}{2}$

Step 2

Move all terms containing $z$ to the left side of the equation.

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Step 2.1

Add $\frac{z}{2}$ to both sides of the equation.

$\frac{5 z}{4} + \frac{z}{2} = 14$

Step 2.2

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

$\frac{5 z}{4} + \frac{z}{2} \cdot \frac{2}{2} = 14$

Step 2.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

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

$\frac{5 z}{4} + \frac{z \cdot 2}{2 \cdot 2} = 14$

Step 2.3.2

Multiply $2$ by $2$ .

$\frac{5 z}{4} + \frac{z \cdot 2}{4} = 14$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 z + z \cdot 2}{4} = 14$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $2$ to the left of $z$ .

$\frac{5 z + 2 \cdot z}{4} = 14$

Step 2.5.2

Add $5 z$ and $2 z$ .

$\frac{7 z}{4} = 14$

Step 3

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 z}{4} = \frac{4}{7} \cdot 14$

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

Simplify $\frac{4}{7} \cdot \frac{7 z}{4}$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{7} \cdot \frac{7 z}{4} = \frac{4}{7} \cdot 14$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 z) = \frac{4}{7} \cdot 14$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 z$ .

$\frac{1}{7} (7 (z)) = \frac{4}{7} \cdot 14$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 z) = \frac{4}{7} \cdot 14$

Step 4.1.1.2.3

Rewrite the expression.

$z = \frac{4}{7} \cdot 14$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{7} \cdot 14$ .

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Step 4.2.1.1

Cancel the common factor of $7$ .

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Step 4.2.1.1.1

Factor $7$ out of $14$ .

$z = \frac{4}{7} \cdot (7 (2))$

Step 4.2.1.1.2

Cancel the common factor.

$z = \frac{4}{7} \cdot (7 \cdot 2)$

Step 4.2.1.1.3

Rewrite the expression.

$z = 4 \cdot 2$

Step 4.2.1.2

Multiply $4$ by $2$ .

$z = 8$