Solve for x 2x+3(x-2)=6(x-1)-x

$2 x + 3 (x - 2) = 6 (x - 1) - x$

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

Simplify each term.

Apply the distributive property.

$2 x + 3 x + 3 \cdot - 2 = 6 (x - 1) - x$

Multiply $3$ by $- 2$ .

$2 x + 3 x - 6 = 6 (x - 1) - x$

Add $2 x$ and $3 x$ .

$5 x - 6 = 6 (x - 1) - x$

Simplify $6 (x - 1) - x$ .

Simplify each term.

Apply the distributive property.

$5 x - 6 = 6 x + 6 \cdot - 1 - x$

Multiply $6$ by $- 1$ .

$5 x - 6 = 6 x - 6 - x$

Subtract $x$ from $6 x$ .

$5 x - 6 = 5 x - 6$

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

Subtract $5 x$ from both sides of the equation.

$5 x - 6 - 5 x = - 6$

Combine the opposite terms in $5 x - 6 - 5 x$ .

Subtract $5 x$ from $5 x$ .

$0 - 6 = - 6$

Subtract $6$ from $0$ .

$- 6 = - 6$

Since $- 6 = - 6$ , 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:

$(- \infty, \infty)$