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

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

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

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

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

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

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

$$2x-2+6+3x=x$$

Add -2 and 6 to get 4.

$$2x+4+3x=x$$

Combine 2x and 3x to get 5x.

$$5x+4=x$$

Subtract x from both sides.

$$5x+4-x=0$$

Combine 5x and -x to get 4x.

$$4x+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$4x=-4$$

Divide both sides by 4.

$$x=\frac{-4}{4}$$

Divide -4 by 4 to get -1.

$$x=-1$$