Solve for x 4x+2(2x-3)=4(2x-2)+2

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 3$ .

$4 x + 4 x - 6 = 4 (2 x - 2) + 2$

Add $4 x$ and $4 x$ .

$8 x - 6 = 4 (2 x - 2) + 2$

Step 2

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

Simplify each term.

Apply the distributive property.

$8 x - 6 = 4 (2 x) + 4 \cdot - 2 + 2$

Multiply $2$ by $4$ .

$8 x - 6 = 8 x + 4 \cdot - 2 + 2$

Multiply $4$ by $- 2$ .

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

Add $- 8$ and $2$ .

$8 x - 6 = 8 x - 6$

Step 3

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

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

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

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

Subtract $8 x$ from $8 x$ .

$0 - 6 = - 6$

Subtract $6$ from $0$ .

$- 6 = - 6$

Step 4

Since $- 6 = - 6$ , 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:

$(- \infty, \infty)$