Basic Math Examples

$\frac{6}{11} d + 4 = \frac{2}{11} d + 16$

Step 1

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

$\frac{6 d}{11} + 4 = \frac{2}{11} d + 16$

Step 2

Combine $\frac{2}{11}$ and $d$ .

$\frac{6 d}{11} + 4 = \frac{2 d}{11} + 16$

Step 3

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

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Step 3.1

Subtract $\frac{2 d}{11}$ from both sides of the equation.

$\frac{6 d}{11} + 4 - \frac{2 d}{11} = 16$

Step 3.2

Combine the numerators over the common denominator.

$4 + \frac{6 d - 2 d}{11} = 16$

Step 3.3

Subtract $2 d$ from $6 d$ .

$4 + \frac{4 d}{11} = 16$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

$\frac{4 d}{11} = 16 - 4$

Step 4.2

Subtract $4$ from $16$ .

$\frac{4 d}{11} = 12$

Step 5

Multiply both sides of the equation by $\frac{11}{4}$ .

$\frac{11}{4} \cdot \frac{4 d}{11} = \frac{11}{4} \cdot 12$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{11}{4} \cdot \frac{4 d}{11}$ .

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Step 6.1.1.1

Cancel the common factor of $11$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{11}{4} \cdot \frac{4 d}{11} = \frac{11}{4} \cdot 12$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 d) = \frac{11}{4} \cdot 12$

Step 6.1.1.2

Cancel the common factor of $4$ .

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Step 6.1.1.2.1

Factor $4$ out of $4 d$ .

$\frac{1}{4} (4 (d)) = \frac{11}{4} \cdot 12$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 d) = \frac{11}{4} \cdot 12$

Step 6.1.1.2.3

Rewrite the expression.

$d = \frac{11}{4} \cdot 12$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{11}{4} \cdot 12$ .

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Step 6.2.1.1

Cancel the common factor of $4$ .

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Step 6.2.1.1.1

Factor $4$ out of $12$ .

$d = \frac{11}{4} \cdot (4 (3))$

Step 6.2.1.1.2

Cancel the common factor.

$d = \frac{11}{4} \cdot (4 \cdot 3)$

Step 6.2.1.1.3

Rewrite the expression.

$d = 11 \cdot 3$

Step 6.2.1.2

Multiply $11$ by $3$ .

$d = 33$