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

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

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

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

Subtract 12 from -3 to get -15.

$$x-15=3\left(x+1\right)-2\left(3+2x\right)$$

Use the distributive property to multiply 3 by x+1.

$$x-15=3x+3-2\left(3+2x\right)$$

Use the distributive property to multiply -2 by 3+2x.

$$x-15=3x+3-6-4x$$

Subtract 6 from 3 to get -3.

$$x-15=3x-3-4x$$

Combine 3x and -4x to get -x.

$$x-15=-x-3$$

Add x to both sides.

$$x-15+x=-3$$

Combine x and x to get 2x.

$$2x-15=-3$$

Add 15 to both sides.

$$2x=-3+15$$

Add -3 and 15 to get 12.

$$2x=12$$

Divide both sides by 2.

$$x=\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$x=6$$