Solve for c 1/2(c+6)=7

$\frac{1}{2} (c + 6) = 7$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (c + 6)) = 2 \cdot 7$

Simplify both sides of the equation.

Simplify the left side.

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

Apply the distributive property.

$2 (\frac{1}{2} c + \frac{1}{2} \cdot 6) = 2 \cdot 7$

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

$2 (\frac{c}{2} + \frac{1}{2} \cdot 6) = 2 \cdot 7$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$2 (\frac{c}{2} + \frac{1}{2} \cdot (2 (3))) = 2 \cdot 7$

Cancel the common factor.

$2 (\frac{c}{2} + \frac{1}{2} \cdot (2 \cdot 3)) = 2 \cdot 7$

Rewrite the expression.

$2 (\frac{c}{2} + 3) = 2 \cdot 7$

Apply the distributive property.

$2 \frac{c}{2} + 2 \cdot 3 = 2 \cdot 7$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{c}{2} + 2 \cdot 3 = 2 \cdot 7$

Rewrite the expression.

$c + 2 \cdot 3 = 2 \cdot 7$

Multiply $2$ by $3$ .

$c + 6 = 2 \cdot 7$

Simplify the right side.

Multiply $2$ by $7$ .

$c + 6 = 14$

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

Subtract $6$ from both sides of the equation.

$c = 14 - 6$

Subtract $6$ from $14$ .

$c = 8$