Solve by Factoring 8(w-1)-4=4(2w-3)

$8 (w - 1) - 4 = 4 (2 w - 3)$

Step 1

Subtract $4 (2 w - 3)$ from both sides of the equation.

$8 (w - 1) - 4 - 4 (2 w - 3) = 0$

Step 2

Simplify $8 (w - 1) - 4 - 4 (2 w - 3)$ .

Simplify each term.

Apply the distributive property.

$8 w + 8 \cdot - 1 - 4 - 4 (2 w - 3) = 0$

Multiply $8$ by $- 1$ .

$8 w - 8 - 4 - 4 (2 w - 3) = 0$

Apply the distributive property.

$8 w - 8 - 4 - 4 (2 w) - 4 \cdot - 3 = 0$

Multiply $2$ by $- 4$ .

$8 w - 8 - 4 - 8 w - 4 \cdot - 3 = 0$

Multiply $- 4$ by $- 3$ .

$8 w - 8 - 4 - 8 w + 12 = 0$

Combine the opposite terms in $8 w - 8 - 4 - 8 w + 12$ .

Subtract $8 w$ from $8 w$ .

$0 - 8 - 4 + 12 = 0$

Subtract $8$ from $0$ .

$- 8 - 4 + 12 = 0$

Subtract $4$ from $- 8$ .

$- 12 + 12 = 0$

Add $- 12$ and $12$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true