Solve for x 4(3-x)+6x=3x+12-x

$4 (3 - x) + 6 x = 3 x + 12 - x$

Step 1

Simplify $4 (3 - x) + 6 x$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 3 + 4 (- x) + 6 x = 3 x + 12 - x$

Multiply $4$ by $3$ .

$12 + 4 (- x) + 6 x = 3 x + 12 - x$

Multiply $- 1$ by $4$ .

$12 - 4 x + 6 x = 3 x + 12 - x$

Add $- 4 x$ and $6 x$ .

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

Step 2

Subtract $x$ from $3 x$ .

$12 + 2 x = 2 x + 12$

Step 3

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

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

$12 + 2 x - 2 x = 12$

Combine the opposite terms in $12 + 2 x - 2 x$ .

Subtract $2 x$ from $2 x$ .

$12 + 0 = 12$

Add $12$ and $0$ .

$12 = 12$

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:

$(- \infty, \infty)$