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

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

Solve for x

$$x=-8$$

Steps for Solving Linear Equation

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

$$2x-\left(x-2\right)=3x+18$$

To find the opposite of x-2, find the opposite of each term.

$$2x-x-\left(-2\right)=3x+18$$

The opposite of -2 is 2.

$$2x-x+2=3x+18$$

Combine 2x and -x to get x.

$$x+2=3x+18$$

Subtract 3x from both sides.

$$x+2-3x=18$$

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

$$-2x+2=18$$

Subtract 2 from both sides.

$$-2x=18-2$$

Subtract 2 from 18 to get 16.

$$-2x=16$$

Divide both sides by -2.

$$x=\frac{16}{-2}$$

Divide 16 by -2 to get -8.

$$x=-8$$