Solve x+3/6+2x-1/3+1/4=x-5/12-frac{2}{3}

$$\frac { x + 3 } { 6 } + \frac { 2 x - 1 } { 3 } + \frac { 1 } { 4 } = \frac { x - 5 } { 12 } - \frac { 2 } { 3 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

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

$$2\left(x+3\right)+4\left(2x-1\right)+3=x-5-8$$

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

$$2x+6+4\left(2x-1\right)+3=x-5-8$$

Use the distributive property to multiply 4 by 2x-1.

$$2x+6+8x-4+3=x-5-8$$

Combine 2x and 8x to get 10x.

$$10x+6-4+3=x-5-8$$

Subtract 4 from 6 to get 2.

$$10x+2+3=x-5-8$$

Add 2 and 3 to get 5.

$$10x+5=x-5-8$$

Subtract 8 from -5 to get -13.

$$10x+5=x-13$$

Subtract x from both sides.

$$10x+5-x=-13$$

Combine 10x and -x to get 9x.

$$9x+5=-13$$

Subtract 5 from both sides.

$$9x=-13-5$$

Subtract 5 from -13 to get -18.

$$9x=-18$$

Divide both sides by 9.

$$x=\frac{-18}{9}$$

Divide -18 by 9 to get -2.

$$x=-2$$