Algebra Examples

$\frac{1}{2} (6 g + 2) = 12$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (6 g + 2)) = 2 \cdot 12$

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 $2 (\frac{1}{2} \cdot (6 g + 2))$ .

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Step 2.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} (6 g) + \frac{1}{2} \cdot 2) = 2 \cdot 12$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Factor $2$ out of $6 g$ .

$2 (\frac{1}{2} (2 (3 g)) + \frac{1}{2} \cdot 2) = 2 \cdot 12$

Step 2.1.1.2.2

Cancel the common factor.

$2 (\frac{1}{2} (2 (3 g)) + \frac{1}{2} \cdot 2) = 2 \cdot 12$

Step 2.1.1.2.3

Rewrite the expression.

$2 (3 g + \frac{1}{2} \cdot 2) = 2 \cdot 12$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Cancel the common factor.

$2 (3 g + \frac{1}{2} \cdot 2) = 2 \cdot 12$

Step 2.1.1.3.2

Rewrite the expression.

$2 (3 g + 1) = 2 \cdot 12$

Step 2.1.1.4

Apply the distributive property.

$2 (3 g) + 2 \cdot 1 = 2 \cdot 12$

Step 2.1.1.5

Multiply.

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Step 2.1.1.5.1

Multiply $3$ by $2$ .

$6 g + 2 \cdot 1 = 2 \cdot 12$

Step 2.1.1.5.2

Multiply $2$ by $1$ .

$6 g + 2 = 2 \cdot 12$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $12$ .

$6 g + 2 = 24$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the equation.

$6 g = 24 - 2$

Step 3.2

Subtract $2$ from $24$ .

$6 g = 22$

Step 4

Divide each term in $6 g = 22$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 g = 22$ by $6$ .

$\frac{6 g}{6} = \frac{22}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 g}{6} = \frac{22}{6}$

Step 4.2.1.2

Divide $g$ by $1$ .

$g = \frac{22}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $22$ and $6$ .

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Step 4.3.1.1

Factor $2$ out of $22$ .

$g = \frac{2 (11)}{6}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $6$ .

$g = \frac{2 \cdot 11}{2 \cdot 3}$

Step 4.3.1.2.2

Cancel the common factor.

$g = \frac{2 \cdot 11}{2 \cdot 3}$

Step 4.3.1.2.3

Rewrite the expression.

$g = \frac{11}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$g = \frac{11}{3}$

Decimal Form:

$g = 3.\overline{6}$

Mixed Number Form:

$g = 3 \frac{2}{3}$