Solve for x 1/2(20-8x)=-3(-2-x)+18

$\frac{1}{2} (20 - 8 x) = - 3 (- 2 - x) + 18$

Step 1

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

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (20 - 8 x) = - 3 (- 2 - x) + 18$

Simplify by adding zeros.

$\frac{1}{2} \cdot (20 - 8 x) = - 3 (- 2 - x) + 18$

Apply the distributive property.

$\frac{1}{2} \cdot 20 + \frac{1}{2} (- 8 x) = - 3 (- 2 - x) + 18$

Cancel the common factor of $2$ .

Factor $2$ out of $20$ .

$\frac{1}{2} \cdot (2 (10)) + \frac{1}{2} (- 8 x) = - 3 (- 2 - x) + 18$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 10) + \frac{1}{2} (- 8 x) = - 3 (- 2 - x) + 18$

Rewrite the expression.

$10 + \frac{1}{2} (- 8 x) = - 3 (- 2 - x) + 18$

Cancel the common factor of $2$ .

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

$10 + \frac{1}{2} (2 (- 4 x)) = - 3 (- 2 - x) + 18$

Cancel the common factor.

$10 + \frac{1}{2} (2 (- 4 x)) = - 3 (- 2 - x) + 18$

Rewrite the expression.

$10 - 4 x = - 3 (- 2 - x) + 18$

Step 2

Simplify $- 3 (- 2 - x) + 18$ .

Simplify each term.

Apply the distributive property.

$10 - 4 x = - 3 \cdot - 2 - 3 (- x) + 18$

Multiply $- 3$ by $- 2$ .

$10 - 4 x = 6 - 3 (- x) + 18$

Multiply $- 1$ by $- 3$ .

$10 - 4 x = 6 + 3 x + 18$

Add $6$ and $18$ .

$10 - 4 x = 3 x + 24$

Step 3

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

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

$10 - 4 x - 3 x = 24$

Subtract $3 x$ from $- 4 x$ .

$10 - 7 x = 24$

Step 4

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

Subtract $10$ from both sides of the equation.

$- 7 x = 24 - 10$

Subtract $10$ from $24$ .

$- 7 x = 14$

Step 5

Divide each term in $- 7 x = 14$ by $- 7$ and simplify.

Divide each term in $- 7 x = 14$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{14}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{14}{- 7}$

Divide $x$ by $1$ .

$x = \frac{14}{- 7}$

Simplify the right side.

Divide $14$ by $- 7$ .

$x = - 2$

Solve for x 1/2(20-8x)=-3(-2-x)+18

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