Solve for x 1/2(x+6)=18

$\frac{1}{2} (x + 6) = 18$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (x + 6)) = 2 \cdot 18$

Simplify both sides of the equation.

Simplify the left side.

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

Apply the distributive property.

$2 (\frac{1}{2} x + \frac{1}{2} \cdot 6) = 2 \cdot 18$

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

$2 (\frac{x}{2} + \frac{1}{2} \cdot 6) = 2 \cdot 18$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$2 (\frac{x}{2} + \frac{1}{2} \cdot (2 (3))) = 2 \cdot 18$

Cancel the common factor.

$2 (\frac{x}{2} + \frac{1}{2} \cdot (2 \cdot 3)) = 2 \cdot 18$

Rewrite the expression.

$2 (\frac{x}{2} + 3) = 2 \cdot 18$

Apply the distributive property.

$2 \frac{x}{2} + 2 \cdot 3 = 2 \cdot 18$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} + 2 \cdot 3 = 2 \cdot 18$

Rewrite the expression.

$x + 2 \cdot 3 = 2 \cdot 18$

Multiply $2$ by $3$ .

$x + 6 = 2 \cdot 18$

Simplify the right side.

Multiply $2$ by $18$ .

$x + 6 = 36$

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

Subtract $6$ from both sides of the equation.

$x = 36 - 6$

Subtract $6$ from $36$ .

$x = 30$