Algebra Examples

$\frac{3}{4} (z + 11) = 27$

Step 1

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} (\frac{3}{4} \cdot (z + 11)) = \frac{4}{3} \cdot 27$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{4}{3} (\frac{3}{4} \cdot (z + 11))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{4}{3} (\frac{3}{4} z + \frac{3}{4} \cdot 11) = \frac{4}{3} \cdot 27$

Step 2.1.1.2

Combine $\frac{3}{4}$ and $z$ .

$\frac{4}{3} (\frac{3 z}{4} + \frac{3}{4} \cdot 11) = \frac{4}{3} \cdot 27$

Step 2.1.1.3

Multiply $\frac{3}{4} \cdot 11$ .

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Step 2.1.1.3.1

Combine $\frac{3}{4}$ and $11$ .

$\frac{4}{3} (\frac{3 z}{4} + \frac{3 \cdot 11}{4}) = \frac{4}{3} \cdot 27$

Step 2.1.1.3.2

Multiply $3$ by $11$ .

$\frac{4}{3} (\frac{3 z}{4} + \frac{33}{4}) = \frac{4}{3} \cdot 27$

Step 2.1.1.4

Apply the distributive property.

$\frac{4}{3} \cdot \frac{3 z}{4} + \frac{4}{3} \cdot \frac{33}{4} = \frac{4}{3} \cdot 27$

Step 2.1.1.5

Cancel the common factor of $4$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 z}{4} + \frac{4}{3} \cdot \frac{33}{4} = \frac{4}{3} \cdot 27$

Step 2.1.1.5.2

Rewrite the expression.

$\frac{1}{3} (3 z) + \frac{4}{3} \cdot \frac{33}{4} = \frac{4}{3} \cdot 27$

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

Factor $3$ out of $3 z$ .

$\frac{1}{3} (3 (z)) + \frac{4}{3} \cdot \frac{33}{4} = \frac{4}{3} \cdot 27$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{1}{3} (3 z) + \frac{4}{3} \cdot \frac{33}{4} = \frac{4}{3} \cdot 27$

Step 2.1.1.6.3

Rewrite the expression.

$z + \frac{4}{3} \cdot \frac{33}{4} = \frac{4}{3} \cdot 27$

Step 2.1.1.7

Cancel the common factor of $4$ .

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Step 2.1.1.7.1

Cancel the common factor.

$z + \frac{4}{3} \cdot \frac{33}{4} = \frac{4}{3} \cdot 27$

Step 2.1.1.7.2

Rewrite the expression.

$z + \frac{1}{3} \cdot 33 = \frac{4}{3} \cdot 27$

Step 2.1.1.8

Cancel the common factor of $3$ .

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Step 2.1.1.8.1

Factor $3$ out of $33$ .

$z + \frac{1}{3} \cdot (3 (11)) = \frac{4}{3} \cdot 27$

Step 2.1.1.8.2

Cancel the common factor.

$z + \frac{1}{3} \cdot (3 \cdot 11) = \frac{4}{3} \cdot 27$

Step 2.1.1.8.3

Rewrite the expression.

$z + 11 = \frac{4}{3} \cdot 27$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{4}{3} \cdot 27$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Factor $3$ out of $27$ .

$z + 11 = \frac{4}{3} \cdot (3 (9))$

Step 2.2.1.1.2

Cancel the common factor.

$z + 11 = \frac{4}{3} \cdot (3 \cdot 9)$

Step 2.2.1.1.3

Rewrite the expression.

$z + 11 = 4 \cdot 9$

Step 2.2.1.2

Multiply $4$ by $9$ .

$z + 11 = 36$

Step 3

Move all terms not containing $z$ to the right side of the equation.

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Step 3.1

Subtract $11$ from both sides of the equation.

$z = 36 - 11$

Step 3.2

Subtract $11$ from $36$ .

$z = 25$