Solve -x-6/2-4-x/6-2=2x+1/3+x

$$- \frac { x - 6 } { 2 } - \frac { 4 - x } { 6 } - 2 = \frac { 2 x + 1 } { 3 } + x$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,6,3.

$$-3\left(x-6\right)-\left(4-x\right)-12=2\left(2x+1\right)+6x$$

Use the distributive property to multiply -3 by x-6.

$$-3x+18-\left(4-x\right)-12=2\left(2x+1\right)+6x$$

To find the opposite of 4-x, find the opposite of each term.

$$-3x+18-4-\left(-x\right)-12=2\left(2x+1\right)+6x$$

The opposite of -x is x.

$$-3x+18-4+x-12=2\left(2x+1\right)+6x$$

Subtract 4 from 18 to get 14.

$$-3x+14+x-12=2\left(2x+1\right)+6x$$

Combine -3x and x to get -2x.

$$-2x+14-12=2\left(2x+1\right)+6x$$

Subtract 12 from 14 to get 2.

$$-2x+2=2\left(2x+1\right)+6x$$

Use the distributive property to multiply 2 by 2x+1.

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

Combine 4x and 6x to get 10x.

$$-2x+2=10x+2$$

Subtract 10x from both sides.

$$-2x+2-10x=2$$

Combine -2x and -10x to get -12x.

$$-12x+2=2$$

Subtract 2 from both sides.

$$-12x=2-2$$

Subtract 2 from 2 to get 0.

$$-12x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -12 is not equal to 0, x must be equal to 0.

$$x=0$$