Solve x/2-x/3+x/4-x/6=frac{3x-6}{4}+x

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4,6.

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

Combine 6x and -4x to get 2x.

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

Combine 2x and 3x to get 5x.

$$5x-2x=3\left(3x-6\right)+12x$$

Combine 5x and -2x to get 3x.

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

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

$$3x=9x-18+12x$$

Combine 9x and 12x to get 21x.

$$3x=21x-18$$

Subtract 21x from both sides.

$$3x-21x=-18$$

Combine 3x and -21x to get -18x.

$$-18x=-18$$

Divide both sides by -18.

$$x=\frac{-18}{-18}$$

Divide -18 by -18 to get 1.

$$x=1$$