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

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

Step 1

Simplify $8 (x - 1) - 4$ .

Simplify each term.

Apply the distributive property.

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

Multiply $8$ by $- 1$ .

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

Subtract $4$ from $- 8$ .

$8 x - 12 = 4 (2 x - 3)$

Step 2

Simplify $4 (2 x - 3)$ .

Apply the distributive property.

$8 x - 12 = 4 (2 x) + 4 \cdot - 3$

Multiply.

Multiply $2$ by $4$ .

$8 x - 12 = 8 x + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$8 x - 12 = 8 x - 12$

Step 3

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

Subtract $8 x$ from both sides of the equation.

$8 x - 12 - 8 x = - 12$

Combine the opposite terms in $8 x - 12 - 8 x$ .

Subtract $8 x$ from $8 x$ .

$0 - 12 = - 12$

Subtract $12$ from $0$ .

$- 12 = - 12$

Step 4

Since $- 12 = - 12$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$