Solve for x 1/2(2x+6)=3x+13

$\frac{1}{2} (2 x + 6) = 3 x + 13$

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

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (2 x + 6) = 3 x + 13$

Simplify by adding zeros.

$\frac{1}{2} \cdot (2 x + 6) = 3 x + 13$

Apply the distributive property.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot 6 = 3 x + 13$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) + \frac{1}{2} \cdot 6 = 3 x + 13$

Cancel the common factor.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot 6 = 3 x + 13$

Rewrite the expression.

$x + \frac{1}{2} \cdot 6 = 3 x + 13$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$x + \frac{1}{2} \cdot (2 (3)) = 3 x + 13$

Cancel the common factor.

$x + \frac{1}{2} \cdot (2 \cdot 3) = 3 x + 13$

Rewrite the expression.

$x + 3 = 3 x + 13$

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$x + 3 - 3 x = 13$

Subtract $3 x$ from $x$ .

$- 2 x + 3 = 13$

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

Subtract $3$ from both sides of the equation.

$- 2 x = 13 - 3$

Subtract $3$ from $13$ .

$- 2 x = 10$

Divide each term in $- 2 x = 10$ by $- 2$ and simplify.

Divide each term in $- 2 x = 10$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

Divide $x$ by $1$ .

$x = \frac{10}{- 2}$

Simplify the right side.

Divide $10$ by $- 2$ .

$x = - 5$