Solve for x 1/2(6x+4)=5(2x-8)

$\frac{1}{2} (6 x + 4) = 5 (2 x - 8)$

Simplify $\frac{1}{2} \cdot (6 x + 4)$ .

Start simplifying.

$0 + 0 + \frac{1}{2} \cdot (6 x + 4) = 5 (2 x - 8)$

Simplify by adding zeros.

$\frac{1}{2} \cdot (6 x + 4) = 5 (2 x - 8)$

Apply the distributive property.

$\frac{1}{2} (6 x) + \frac{1}{2} \cdot 4 = 5 (2 x - 8)$

Cancel the common factor of $2$ .

Factor $2$ out of $6 x$ .

$\frac{1}{2} (2 (3 x)) + \frac{1}{2} \cdot 4 = 5 (2 x - 8)$

Cancel the common factor.

$\frac{1}{2} (2 (3 x)) + \frac{1}{2} \cdot 4 = 5 (2 x - 8)$

Rewrite the expression.

$3 x + \frac{1}{2} \cdot 4 = 5 (2 x - 8)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$3 x + \frac{1}{2} \cdot (2 (2)) = 5 (2 x - 8)$

Cancel the common factor.

$3 x + \frac{1}{2} \cdot (2 \cdot 2) = 5 (2 x - 8)$

Rewrite the expression.

$3 x + 2 = 5 (2 x - 8)$

Simplify $5 (2 x - 8)$ .

Apply the distributive property.

$3 x + 2 = 5 (2 x) + 5 \cdot - 8$

Multiply.

Multiply $2$ by $5$ .

$3 x + 2 = 10 x + 5 \cdot - 8$

Multiply $5$ by $- 8$ .

$3 x + 2 = 10 x - 40$

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

Subtract $10 x$ from both sides of the equation.

$3 x + 2 - 10 x = - 40$

Subtract $10 x$ from $3 x$ .

$- 7 x + 2 = - 40$

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

Subtract $2$ from both sides of the equation.

$- 7 x = - 40 - 2$

Subtract $2$ from $- 40$ .

$- 7 x = - 42$

Divide each term in $- 7 x = - 42$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 42$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 42}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 42}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 42}{- 7}$

Simplify the right side.

Divide $- 42$ by $- 7$ .

$x = 6$

Solve for x 1/2(6x+4)=5(2x-8)

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