Solve for x 4(0.5x-3)=x-0.25(12-8x)

$4 (0.5 x - 3) = x - 0.25 (12 - 8 x)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x - 0.25 (12 - 8 x) = 4 (0.5 x - 3)$

Step 2

Simplify $x - 0.25 (12 - 8 x)$ .

Simplify each term.

Apply the distributive property.

$x - 0.25 \cdot 12 - 0.25 (- 8 x) = 4 (0.5 x - 3)$

Multiply $- 0.25$ by $12$ .

$x - 3 - 0.25 (- 8 x) = 4 (0.5 x - 3)$

Multiply $- 8$ by $- 0.25$ .

$x - 3 + 2 x = 4 (0.5 x - 3)$

Add $x$ and $2 x$ .

$3 x - 3 = 4 (0.5 x - 3)$

Step 3

Simplify $4 (0.5 x - 3)$ .

Apply the distributive property.

$3 x - 3 = 4 (0.5 x) + 4 \cdot - 3$

Multiply.

Multiply $0.5$ by $4$ .

$3 x - 3 = 2 x + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$3 x - 3 = 2 x - 12$

Step 4

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

Subtract $2 x$ from both sides of the equation.

$3 x - 3 - 2 x = - 12$

Subtract $2 x$ from $3 x$ .

$x - 3 = - 12$

Step 5

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

Add $3$ to both sides of the equation.

$x = - 12 + 3$

Add $- 12$ and $3$ .

$x = - 9$