Solve for n 1/2(n+4)=6

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

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.

Simplify the left side.

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

Apply the distributive property.

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $2$ .

$n + 4 = 2 \cdot 6$

Simplify the right side.

Multiply $2$ by $6$ .

$n + 4 = 12$

Step 3

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

Subtract $4$ from both sides of the equation.

$n = 12 - 4$

Subtract $4$ from $12$ .

$n = 8$