Solve x+4/2-2/4-2x/8=x+6/12-frac{x}{6}

$$\frac { x + 4 } { 2 } - \frac { 2 } { 4 } - \frac { 2 x } { 8 } = \frac { x + 6 } { 12 } - \frac { x } { 6 }$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 2,4,8,12,6.

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

Use the distributive property to multiply 12 by x+4.

$$12x+48-6\times 2-3\times 2x=2\left(x+6\right)-4x$$

Multiply -6 and 2 to get -12.

$$12x+48-12-3\times 2x=2\left(x+6\right)-4x$$

Subtract 12 from 48 to get 36.

$$12x+36-3\times 2x=2\left(x+6\right)-4x$$

Multiply -3 and 2 to get -6.

$$12x+36-6x=2\left(x+6\right)-4x$$

Combine 12x and -6x to get 6x.

$$6x+36=2\left(x+6\right)-4x$$

Use the distributive property to multiply 2 by x+6.

$$6x+36=2x+12-4x$$

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

$$6x+36=-2x+12$$

Add 2x to both sides.

$$6x+36+2x=12$$

Combine 6x and 2x to get 8x.

$$8x+36=12$$

Subtract 36 from both sides.

$$8x=12-36$$

Subtract 36 from 12 to get -24.

$$8x=-24$$

Divide both sides by 8.

$$x=\frac{-24}{8}$$

Divide -24 by 8 to get -3.

$$x=-3$$