Solve for x 1/2(-10x+4)=-4(-3+2x)+8

$\frac{1}{2} (- 10 x + 4) = - 4 (- 3 + 2 x) + 8$

Step 1

Simplify $\frac{1}{2} \cdot (- 10 x + 4)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (- 10 x + 4) = - 4 (- 3 + 2 x) + 8$

Simplify by adding zeros.

$\frac{1}{2} \cdot (- 10 x + 4) = - 4 (- 3 + 2 x) + 8$

Apply the distributive property.

$\frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 4 = - 4 (- 3 + 2 x) + 8$

Cancel the common factor of $2$ .

Factor $2$ out of $- 10 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 5 x + 2 = - 4 (- 3 + 2 x) + 8$

Step 2

Simplify $- 4 (- 3 + 2 x) + 8$ .

Simplify each term.

Apply the distributive property.

$- 5 x + 2 = - 4 \cdot - 3 - 4 (2 x) + 8$

Multiply $- 4$ by $- 3$ .

$- 5 x + 2 = 12 - 4 (2 x) + 8$

Multiply $2$ by $- 4$ .

$- 5 x + 2 = 12 - 8 x + 8$

Add $12$ and $8$ .

$- 5 x + 2 = - 8 x + 20$

Step 3

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

Add $8 x$ to both sides of the equation.

$- 5 x + 2 + 8 x = 20$

Add $- 5 x$ and $8 x$ .

$3 x + 2 = 20$

Step 4

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

Subtract $2$ from both sides of the equation.

$3 x = 20 - 2$

Subtract $2$ from $20$ .

$3 x = 18$

Step 5

Divide each term in $3 x = 18$ by $3$ and simplify.

Divide each term in $3 x = 18$ by $3$ .

$\frac{3 x}{3} = \frac{18}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{18}{3}$

Divide $x$ by $1$ .

$x = \frac{18}{3}$

Simplify the right side.

Divide $18$ by $3$ .

$x = 6$

Solve for x 1/2(-10x+4)=-4(-3+2x)+8

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