Algebra Examples

$\frac{1}{4} (\frac{1}{3} k + 9) = 6$

Step 1

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} \cdot (\frac{1}{3} k + 9)) = 4 \cdot 6$

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 $4 (\frac{1}{4} \cdot (\frac{1}{3} k + 9))$ .

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Step 2.1.1.1

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

$4 (\frac{1}{4} \cdot (\frac{k}{3} + 9)) = 4 \cdot 6$

Step 2.1.1.2

Apply the distributive property.

$4 (\frac{1}{4} \cdot \frac{k}{3} + \frac{1}{4} \cdot 9) = 4 \cdot 6$

Step 2.1.1.3

Multiply $\frac{1}{4} \cdot \frac{k}{3}$ .

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Step 2.1.1.3.1

Multiply $\frac{1}{4}$ by $\frac{k}{3}$ .

$4 (\frac{k}{4 \cdot 3} + \frac{1}{4} \cdot 9) = 4 \cdot 6$

Step 2.1.1.3.2

Multiply $4$ by $3$ .

$4 (\frac{k}{12} + \frac{1}{4} \cdot 9) = 4 \cdot 6$

Step 2.1.1.4

Combine $\frac{1}{4}$ and $9$ .

$4 (\frac{k}{12} + \frac{9}{4}) = 4 \cdot 6$

Step 2.1.1.5

Apply the distributive property.

$4 \frac{k}{12} + 4 (\frac{9}{4}) = 4 \cdot 6$

Step 2.1.1.6

Cancel the common factor of $4$ .

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Step 2.1.1.6.1

Factor $4$ out of $12$ .

$4 \frac{k}{4 (3)} + 4 (\frac{9}{4}) = 4 \cdot 6$

Step 2.1.1.6.2

Cancel the common factor.

$4 \frac{k}{4 \cdot 3} + 4 (\frac{9}{4}) = 4 \cdot 6$

Step 2.1.1.6.3

Rewrite the expression.

$\frac{k}{3} + 4 (\frac{9}{4}) = 4 \cdot 6$

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.

$\frac{k}{3} + 4 (\frac{9}{4}) = 4 \cdot 6$

Step 2.1.1.7.2

Rewrite the expression.

$\frac{k}{3} + 9 = 4 \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $4$ by $6$ .

$\frac{k}{3} + 9 = 24$

Step 3

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

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Step 3.1

Subtract $9$ from both sides of the equation.

$\frac{k}{3} = 24 - 9$

Step 3.2

Subtract $9$ from $24$ .

$\frac{k}{3} = 15$

Step 4

Multiply both sides of the equation by $3$ .

$3 \frac{k}{3} = 3 \cdot 15$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1

Cancel the common factor.

$3 \frac{k}{3} = 3 \cdot 15$

Step 5.1.1.2

Rewrite the expression.

$k = 3 \cdot 15$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $3$ by $15$ .

$k = 45$