Algebra Examples

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

Step 1

Rewrite the equation as $\frac{1}{4} \cdot (6 x + 12) = 9$ .

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

Step 2

Multiply both sides of the equation by $4$ .

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $4 (\frac{1}{4} \cdot (6 x + 12))$ .

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Step 3.1.1.1

Apply the distributive property.

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

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $4$ .

$4 (\frac{1}{2 (2)} (6 x) + \frac{1}{4} \cdot 12) = 4 \cdot 9$

Step 3.1.1.2.2

Factor $2$ out of $6 x$ .

$4 (\frac{1}{2 (2)} (2 (3 x)) + \frac{1}{4} \cdot 12) = 4 \cdot 9$

Step 3.1.1.2.3

Cancel the common factor.

$4 (\frac{1}{2 \cdot 2} (2 (3 x)) + \frac{1}{4} \cdot 12) = 4 \cdot 9$

Step 3.1.1.2.4

Rewrite the expression.

$4 (\frac{1}{2} (3 x) + \frac{1}{4} \cdot 12) = 4 \cdot 9$

Step 3.1.1.3

Combine $3$ and $\frac{1}{2}$ .

$4 (\frac{3}{2} x + \frac{1}{4} \cdot 12) = 4 \cdot 9$

Step 3.1.1.4

Combine $\frac{3}{2}$ and $x$ .

$4 (\frac{3 x}{2} + \frac{1}{4} \cdot 12) = 4 \cdot 9$

Step 3.1.1.5

Cancel the common factor of $4$ .

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Step 3.1.1.5.1

Factor $4$ out of $12$ .

$4 (\frac{3 x}{2} + \frac{1}{4} \cdot (4 (3))) = 4 \cdot 9$

Step 3.1.1.5.2

Cancel the common factor.

$4 (\frac{3 x}{2} + \frac{1}{4} \cdot (4 \cdot 3)) = 4 \cdot 9$

Step 3.1.1.5.3

Rewrite the expression.

$4 (\frac{3 x}{2} + 3) = 4 \cdot 9$

Step 3.1.1.6

Apply the distributive property.

$4 \frac{3 x}{2} + 4 \cdot 3 = 4 \cdot 9$

Step 3.1.1.7

Cancel the common factor of $2$ .

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Step 3.1.1.7.1

Factor $2$ out of $4$ .

$2 (2) \frac{3 x}{2} + 4 \cdot 3 = 4 \cdot 9$

Step 3.1.1.7.2

Cancel the common factor.

$2 \cdot 2 \frac{3 x}{2} + 4 \cdot 3 = 4 \cdot 9$

Step 3.1.1.7.3

Rewrite the expression.

$2 (3 x) + 4 \cdot 3 = 4 \cdot 9$

Step 3.1.1.8

Multiply.

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Step 3.1.1.8.1

Multiply $3$ by $2$ .

$6 x + 4 \cdot 3 = 4 \cdot 9$

Step 3.1.1.8.2

Multiply $4$ by $3$ .

$6 x + 12 = 4 \cdot 9$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $4$ by $9$ .

$6 x + 12 = 36$

Step 4

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

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Step 4.1

Subtract $12$ from both sides of the equation.

$6 x = 36 - 12$

Step 4.2

Subtract $12$ from $36$ .

$6 x = 24$

Step 5

Divide each term in $6 x = 24$ by $6$ and simplify.

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Step 5.1

Divide each term in $6 x = 24$ by $6$ .

$\frac{6 x}{6} = \frac{24}{6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{24}{6}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $24$ by $6$ .

$x = 4$