Basic Math Examples

$z - \frac{1}{3} z - \frac{1}{2} z - 5 = 0$

Step 1

Simplify $z - \frac{1}{3} z - \frac{1}{2} z - 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $z$ and $\frac{1}{3}$ .

$z - \frac{z}{3} - \frac{1}{2} z - 5 = 0$

Step 1.1.2

Combine $z$ and $\frac{1}{2}$ .

$z - \frac{z}{3} - \frac{z}{2} - 5 = 0$

Step 1.2

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

$z \cdot \frac{3}{3} - \frac{z}{3} - \frac{z}{2} - 5 = 0$

Step 1.3

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

$\frac{z \cdot 3}{3} - \frac{z}{3} - \frac{z}{2} - 5 = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{z \cdot 3 - z}{3} - \frac{z}{2} - 5 = 0$

Step 1.5

Subtract $z$ from $z \cdot 3$ .

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Step 1.5.1

Reorder $z$ and $3$ .

$\frac{3 \cdot z - z}{3} - \frac{z}{2} - 5 = 0$

Step 1.5.2

Subtract $z$ from $3 \cdot z$ .

$\frac{2 \cdot z}{3} - \frac{z}{2} - 5 = 0$

Step 1.6

To write $\frac{2 z}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 z}{3} \cdot \frac{2}{2} - \frac{z}{2} - 5 = 0$

Step 1.7

To write $- \frac{z}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 z}{3} \cdot \frac{2}{2} - \frac{z}{2} \cdot \frac{3}{3} - 5 = 0$

Step 1.8

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.8.1

Multiply $\frac{2 z}{3}$ by $\frac{2}{2}$ .

$\frac{2 z \cdot 2}{3 \cdot 2} - \frac{z}{2} \cdot \frac{3}{3} - 5 = 0$

Step 1.8.2

Multiply $3$ by $2$ .

$\frac{2 z \cdot 2}{6} - \frac{z}{2} \cdot \frac{3}{3} - 5 = 0$

Step 1.8.3

Multiply $\frac{z}{2}$ by $\frac{3}{3}$ .

$\frac{2 z \cdot 2}{6} - \frac{z \cdot 3}{2 \cdot 3} - 5 = 0$

Step 1.8.4

Multiply $2$ by $3$ .

$\frac{2 z \cdot 2}{6} - \frac{z \cdot 3}{6} - 5 = 0$

Step 1.9

Combine the numerators over the common denominator.

$\frac{2 z \cdot 2 - z \cdot 3}{6} - 5 = 0$

Step 1.10

Simplify each term.

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Step 1.10.1

Simplify the numerator.

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Step 1.10.1.1

Factor $z$ out of $2 z \cdot 2 - z \cdot 3$ .

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Step 1.10.1.1.1

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

$\frac{z (2 \cdot 2) - z \cdot 3}{6} - 5 = 0$

Step 1.10.1.1.2

Factor $z$ out of $- z \cdot 3$ .

$\frac{z (2 \cdot 2) + z (- 1 \cdot 3)}{6} - 5 = 0$

Step 1.10.1.1.3

Factor $z$ out of $z (2 \cdot 2) + z (- 1 \cdot 3)$ .

$\frac{z (2 \cdot 2 - 1 \cdot 3)}{6} - 5 = 0$

Step 1.10.1.2

Multiply $2$ by $2$ .

$\frac{z (4 - 1 \cdot 3)}{6} - 5 = 0$

Step 1.10.1.3

Multiply $- 1$ by $3$ .

$\frac{z (4 - 3)}{6} - 5 = 0$

Step 1.10.1.4

Subtract $3$ from $4$ .

$\frac{z \cdot 1}{6} - 5 = 0$

Step 1.10.2

Multiply $z$ by $1$ .

$\frac{z}{6} - 5 = 0$

Step 2

Add $5$ to both sides of the equation.

$\frac{z}{6} = 5$

Step 3

Multiply both sides of the equation by $6$ .

$6 \frac{z}{6} = 6 \cdot 5$

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

Cancel the common factor of $6$ .

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Step 4.1.1.1

Cancel the common factor.

$6 \frac{z}{6} = 6 \cdot 5$

Step 4.1.1.2

Rewrite the expression.

$z = 6 \cdot 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $6$ by $5$ .

$z = 30$