Algebra Examples

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

Step 1

Simplify $\frac{1}{4} k$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{4} k = 3 (- \frac{1}{4} k + 3)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

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

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

Step 2

Simplify $3 (- \frac{1}{4} k + 3)$ .

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Step 2.1

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

$\frac{k}{4} = 3 (- \frac{k}{4} + 3)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Multiply $3 (- \frac{k}{4})$ .

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Step 2.3.1

Multiply $- 1$ by $3$ .

$\frac{k}{4} = - 3 \frac{k}{4} + 3 \cdot 3$

Step 2.3.2

Combine $- 3$ and $\frac{k}{4}$ .

$\frac{k}{4} = \frac{- 3 k}{4} + 3 \cdot 3$

Step 2.4

Multiply $3$ by $3$ .

$\frac{k}{4} = \frac{- 3 k}{4} + 9$

Step 2.5

Move the negative in front of the fraction.

$\frac{k}{4} = - \frac{3 k}{4} + 9$

Step 3

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

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Step 3.1

Add $\frac{3 k}{4}$ to both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Add $k$ and $3 k$ .

$\frac{4 k}{4} = 9$

Step 3.4

Cancel the common factor of $4$ .

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Step 3.4.1

Cancel the common factor.

$\frac{4 k}{4} = 9$

Step 3.4.2

Divide $k$ by $1$ .

$k = 9$