Solve for x 1/2(20-8x)=-2(-2+x)+2

$\frac{1}{2} (20 - 8 x) = - 2 (- 2 + x) + 2$

Simplify $\frac{1}{2} \cdot (20 - 8 x)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (20 - 8 x) = - 2 (- 2 + x) + 2$

Simplify by adding zeros.

$\frac{1}{2} \cdot (20 - 8 x) = - 2 (- 2 + x) + 2$

Apply the distributive property.

$\frac{1}{2} \cdot 20 + \frac{1}{2} (- 8 x) = - 2 (- 2 + x) + 2$

Cancel the common factor of $2$ .

Factor $2$ out of $20$ .

$\frac{1}{2} \cdot (2 (10)) + \frac{1}{2} (- 8 x) = - 2 (- 2 + x) + 2$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 10) + \frac{1}{2} (- 8 x) = - 2 (- 2 + x) + 2$

Rewrite the expression.

$10 + \frac{1}{2} (- 8 x) = - 2 (- 2 + x) + 2$

Cancel the common factor of $2$ .

Factor $2$ out of $- 8 x$ .

$10 + \frac{1}{2} (2 (- 4 x)) = - 2 (- 2 + x) + 2$

Cancel the common factor.

$10 + \frac{1}{2} (2 (- 4 x)) = - 2 (- 2 + x) + 2$

Rewrite the expression.

$10 - 4 x = - 2 (- 2 + x) + 2$

Simplify $- 2 (- 2 + x) + 2$ .

Simplify each term.

Apply the distributive property.

$10 - 4 x = - 2 \cdot - 2 - 2 x + 2$

Multiply $- 2$ by $- 2$ .

$10 - 4 x = 4 - 2 x + 2$

Add $4$ and $2$ .

$10 - 4 x = - 2 x + 6$

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

Add $2 x$ to both sides of the equation.

$10 - 4 x + 2 x = 6$

Add $- 4 x$ and $2 x$ .

$10 - 2 x = 6$

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

Subtract $10$ from both sides of the equation.

$- 2 x = 6 - 10$

Subtract $10$ from $6$ .

$- 2 x = - 4$

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x = 2$

Solve for x 1/2(20-8x)=-2(-2+x)+2

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