Basic Math Examples

$\frac{z}{2} = \frac{z}{3} + 4$

Step 1

Multiply both sides by $2$ .

$\frac{z}{2} \cdot 2 = (\frac{z}{3} + 4) \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{z}{2} \cdot 2 = (\frac{z}{3} + 4) \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$z = (\frac{z}{3} + 4) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{z}{3} + 4) \cdot 2$ .

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Step 2.2.1.1

Simplify terms.

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Step 2.2.1.1.1

Apply the distributive property.

$z = \frac{z}{3} \cdot 2 + 4 \cdot 2$

Step 2.2.1.1.2

Combine $\frac{z}{3}$ and $2$ .

$z = \frac{z \cdot 2}{3} + 4 \cdot 2$

Step 2.2.1.1.3

Multiply $4$ by $2$ .

$z = \frac{z \cdot 2}{3} + 8$

Step 2.2.1.2

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

$z = \frac{2 z}{3} + 8$

Step 3

Solve for $z$ .

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Step 3.1

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

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Step 3.1.1

Subtract $\frac{2 z}{3}$ from both sides of the equation.

$z - \frac{2 z}{3} = 8$

Step 3.1.2

To write $z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$z \cdot \frac{3}{3} - \frac{2 z}{3} = 8$

Step 3.1.3

Combine $z$ and $\frac{3}{3}$ .

$\frac{z \cdot 3}{3} - \frac{2 z}{3} = 8$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{z \cdot 3 - 2 z}{3} = 8$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Move $3$ to the left of $z$ .

$\frac{3 \cdot z - 2 z}{3} = 8$

Step 3.1.5.2

Subtract $2 z$ from $3 z$ .

$\frac{z}{3} = 8$

Step 3.2

Multiply both sides of the equation by $3$ .

$3 \frac{z}{3} = 3 \cdot 8$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Cancel the common factor of $3$ .

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Step 3.3.1.1.1

Cancel the common factor.

$3 \frac{z}{3} = 3 \cdot 8$

Step 3.3.1.1.2

Rewrite the expression.

$z = 3 \cdot 8$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $3$ by $8$ .

$z = 24$