Solve for x 3(x-4)=-2+3x-10

$3 (x - 4) = - 2 + 3 x - 10$

Step 1

Simplify $3 (x - 4)$ .

Rewrite.

$0 + 0 + 3 (x - 4) = - 2 + 3 x - 10$

Simplify by adding zeros.

$3 (x - 4) = - 2 + 3 x - 10$

Apply the distributive property.

$3 x + 3 \cdot - 4 = - 2 + 3 x - 10$

Multiply $3$ by $- 4$ .

$3 x - 12 = - 2 + 3 x - 10$

Step 2

Subtract $10$ from $- 2$ .

$3 x - 12 = 3 x - 12$

Step 3

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

Subtract $3 x$ from both sides of the equation.

$3 x - 12 - 3 x = - 12$

Combine the opposite terms in $3 x - 12 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 12 = - 12$

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:

$(- \infty, \infty)$