Solve for x 1/2(4x-8)+3x=36

$\frac{1}{2} (4 x - 8) + 3 x = 36$

Step 1

Simplify $\frac{1}{2} \cdot (4 x - 8) + 3 x$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{2} (4 x) + \frac{1}{2} \cdot - 8 + 3 x = 36$

Cancel the common factor of $2$ .

Factor $2$ out of $4 x$ .

$\frac{1}{2} (2 (2 x)) + \frac{1}{2} \cdot - 8 + 3 x = 36$

Cancel the common factor.

$\frac{1}{2} (2 (2 x)) + \frac{1}{2} \cdot - 8 + 3 x = 36$

Rewrite the expression.

$2 x + \frac{1}{2} \cdot - 8 + 3 x = 36$

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$2 x + \frac{1}{2} \cdot (2 (- 4)) + 3 x = 36$

Cancel the common factor.

$2 x + \frac{1}{2} \cdot (2 \cdot - 4) + 3 x = 36$

Rewrite the expression.

$2 x - 4 + 3 x = 36$

Add $2 x$ and $3 x$ .

$5 x - 4 = 36$

Step 2

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

Add $4$ to both sides of the equation.

$5 x = 36 + 4$

Add $36$ and $4$ .

$5 x = 40$

Step 3

Divide each term in $5 x = 40$ by $5$ and simplify.

Divide each term in $5 x = 40$ by $5$ .

$\frac{5 x}{5} = \frac{40}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{40}{5}$

Divide $x$ by $1$ .

$x = \frac{40}{5}$

Simplify the right side.

Divide $40$ by $5$ .

$x = 8$