Basic Math Examples

$- 2 z + \frac{23}{6} z = \frac{22}{15}$

Step 1

Simplify $- 2 z + \frac{23}{6} z$ .

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Step 1.1

Combine $\frac{23}{6}$ and $z$ .

$- 2 z + \frac{23 z}{6} = \frac{22}{15}$

Step 1.2

To write $- 2 z$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- 2 z \cdot \frac{6}{6} + \frac{23 z}{6} = \frac{22}{15}$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $- 2 z$ and $\frac{6}{6}$ .

$\frac{- 2 z \cdot 6}{6} + \frac{23 z}{6} = \frac{22}{15}$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{- 2 z \cdot 6 + 23 z}{6} = \frac{22}{15}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $z$ out of $- 2 z \cdot 6 + 23 z$ .

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Step 1.4.1.1

Factor $z$ out of $- 2 z \cdot 6$ .

$\frac{z (- 2 \cdot 6) + 23 z}{6} = \frac{22}{15}$

Step 1.4.1.2

Factor $z$ out of $23 z$ .

$\frac{z (- 2 \cdot 6) + z \cdot 23}{6} = \frac{22}{15}$

Step 1.4.1.3

Factor $z$ out of $z (- 2 \cdot 6) + z \cdot 23$ .

$\frac{z (- 2 \cdot 6 + 23)}{6} = \frac{22}{15}$

Step 1.4.2

Multiply $- 2$ by $6$ .

$\frac{z (- 12 + 23)}{6} = \frac{22}{15}$

Step 1.4.3

Add $- 12$ and $23$ .

$\frac{z \cdot 11}{6} = \frac{22}{15}$

Step 1.5

Move $11$ to the left of $z$ .

$\frac{11 z}{6} = \frac{22}{15}$

Step 2

Multiply both sides of the equation by $\frac{6}{11}$ .

$\frac{6}{11} \cdot \frac{11 z}{6} = \frac{6}{11} \cdot \frac{22}{15}$

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 $\frac{6}{11} \cdot \frac{11 z}{6}$ .

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Step 3.1.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{6}{11} \cdot \frac{11 z}{6} = \frac{6}{11} \cdot \frac{22}{15}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 z) = \frac{6}{11} \cdot \frac{22}{15}$

Step 3.1.1.2

Cancel the common factor of $11$ .

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Step 3.1.1.2.1

Factor $11$ out of $11 z$ .

$\frac{1}{11} (11 (z)) = \frac{6}{11} \cdot \frac{22}{15}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 z) = \frac{6}{11} \cdot \frac{22}{15}$

Step 3.1.1.2.3

Rewrite the expression.

$z = \frac{6}{11} \cdot \frac{22}{15}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{6}{11} \cdot \frac{22}{15}$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $6$ .

$z = \frac{3 (2)}{11} \cdot \frac{22}{15}$

Step 3.2.1.1.2

Factor $3$ out of $15$ .

$z = \frac{3 \cdot 2}{11} \cdot \frac{22}{3 \cdot 5}$

Step 3.2.1.1.3

Cancel the common factor.

$z = \frac{3 \cdot 2}{11} \cdot \frac{22}{3 \cdot 5}$

Step 3.2.1.1.4

Rewrite the expression.

$z = \frac{2}{11} \cdot \frac{22}{5}$

Step 3.2.1.2

Cancel the common factor of $11$ .

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Step 3.2.1.2.1

Factor $11$ out of $22$ .

$z = \frac{2}{11} \cdot \frac{11 (2)}{5}$

Step 3.2.1.2.2

Cancel the common factor.

$z = \frac{2}{11} \cdot \frac{11 \cdot 2}{5}$

Step 3.2.1.2.3

Rewrite the expression.

$z = 2 (\frac{2}{5})$

Step 3.2.1.3

Combine $2$ and $\frac{2}{5}$ .

$z = \frac{2 \cdot 2}{5}$

Step 3.2.1.4

Multiply $2$ by $2$ .

$z = \frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{4}{5}$

Decimal Form:

$z = 0.8$