Algebra Examples

$\frac{1}{2} (n + 4) = 6$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (n + 4)) = 2 \cdot 6$

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 $2 (\frac{1}{2} \cdot (n + 4))$ .

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Step 2.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} n + \frac{1}{2} \cdot 4) = 2 \cdot 6$

Step 2.1.1.2

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

$2 (\frac{n}{2} + \frac{1}{2} \cdot 4) = 2 \cdot 6$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $4$ .

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

$2 (\frac{n}{2} + 2) = 2 \cdot 6$

Step 2.1.1.4

Apply the distributive property.

$2 \frac{n}{2} + 2 \cdot 2 = 2 \cdot 6$

Step 2.1.1.5

Cancel the common factor of $2$ .

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Step 2.1.1.5.1

Cancel the common factor.

$2 \frac{n}{2} + 2 \cdot 2 = 2 \cdot 6$

Step 2.1.1.5.2

Rewrite the expression.

$n + 2 \cdot 2 = 2 \cdot 6$

Step 2.1.1.6

Multiply $2$ by $2$ .

$n + 4 = 2 \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $6$ .

$n + 4 = 12$

Step 3

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

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Step 3.1

Subtract $4$ from both sides of the equation.

$n = 12 - 4$

Step 3.2

Subtract $4$ from $12$ .

$n = 8$