Basic Math Examples

$\frac{6}{11} \cdot (v + 5) = 6$

Step 1

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

$\frac{11}{6} (\frac{6}{11} \cdot (v + 5)) = \frac{11}{6} \cdot 6$

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 $\frac{11}{6} (\frac{6}{11} \cdot (v + 5))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{11}{6} (\frac{6}{11} v + \frac{6}{11} \cdot 5) = \frac{11}{6} \cdot 6$

Step 2.1.1.2

Combine $\frac{6}{11}$ and $v$ .

$\frac{11}{6} (\frac{6 v}{11} + \frac{6}{11} \cdot 5) = \frac{11}{6} \cdot 6$

Step 2.1.1.3

Multiply $\frac{6}{11} \cdot 5$ .

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Step 2.1.1.3.1

Combine $\frac{6}{11}$ and $5$ .

$\frac{11}{6} (\frac{6 v}{11} + \frac{6 \cdot 5}{11}) = \frac{11}{6} \cdot 6$

Step 2.1.1.3.2

Multiply $6$ by $5$ .

$\frac{11}{6} (\frac{6 v}{11} + \frac{30}{11}) = \frac{11}{6} \cdot 6$

Step 2.1.1.4

Apply the distributive property.

$\frac{11}{6} \cdot \frac{6 v}{11} + \frac{11}{6} \cdot \frac{30}{11} = \frac{11}{6} \cdot 6$

Step 2.1.1.5

Cancel the common factor of $11$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{11}{6} \cdot \frac{6 v}{11} + \frac{11}{6} \cdot \frac{30}{11} = \frac{11}{6} \cdot 6$

Step 2.1.1.5.2

Rewrite the expression.

$\frac{1}{6} (6 v) + \frac{11}{6} \cdot \frac{30}{11} = \frac{11}{6} \cdot 6$

Step 2.1.1.6

Cancel the common factor of $6$ .

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Step 2.1.1.6.1

Factor $6$ out of $6 v$ .

$\frac{1}{6} (6 (v)) + \frac{11}{6} \cdot \frac{30}{11} = \frac{11}{6} \cdot 6$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{1}{6} (6 v) + \frac{11}{6} \cdot \frac{30}{11} = \frac{11}{6} \cdot 6$

Step 2.1.1.6.3

Rewrite the expression.

$v + \frac{11}{6} \cdot \frac{30}{11} = \frac{11}{6} \cdot 6$

Step 2.1.1.7

Cancel the common factor of $11$ .

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Step 2.1.1.7.1

Cancel the common factor.

$v + \frac{11}{6} \cdot \frac{30}{11} = \frac{11}{6} \cdot 6$

Step 2.1.1.7.2

Rewrite the expression.

$v + \frac{1}{6} \cdot 30 = \frac{11}{6} \cdot 6$

Step 2.1.1.8

Cancel the common factor of $6$ .

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Step 2.1.1.8.1

Factor $6$ out of $30$ .

$v + \frac{1}{6} \cdot (6 (5)) = \frac{11}{6} \cdot 6$

Step 2.1.1.8.2

Cancel the common factor.

$v + \frac{1}{6} \cdot (6 \cdot 5) = \frac{11}{6} \cdot 6$

Step 2.1.1.8.3

Rewrite the expression.

$v + 5 = \frac{11}{6} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$v + 5 = \frac{11}{6} \cdot 6$

Step 2.2.1.2

Rewrite the expression.

$v + 5 = 11$

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the equation.

$v = 11 - 5$

Step 3.2

Subtract $5$ from $11$ .

$v = 6$