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

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 4$ .

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

Add $4 x$ and $2 x$ .

$6 x - 8 = 8 (x - 1) - 2 x$

Simplify $8 (x - 1) - 2 x$ .

Simplify each term.

Apply the distributive property.

$6 x - 8 = 8 x + 8 \cdot - 1 - 2 x$

Multiply $8$ by $- 1$ .

$6 x - 8 = 8 x - 8 - 2 x$

Subtract $2 x$ from $8 x$ .

$6 x - 8 = 6 x - 8$

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

Subtract $6 x$ from both sides of the equation.

$6 x - 8 - 6 x = - 8$

Combine the opposite terms in $6 x - 8 - 6 x$ .

Subtract $6 x$ from $6 x$ .

$0 - 8 = - 8$

Subtract $8$ from $0$ .

$- 8 = - 8$

Since $- 8 = - 8$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$